Alternating Current - Ex # 1 - 4

LEVEL # 1 Questions based on

Q.1

Q.8

Alternating signal

An alternating current changes from a complete cycle in 1s, then the frequency in Hz will be – (A) 10-6 (B) 50 (C) 100 (D) 106

If the value of Erms is 5 volt, then the tolerance of the component in volt is 1

(A) 1 (C) Q.9

(B) 5

5

(D) 5 2

A mixer of 1000 resistance is connected

Q.2

An alternating voltage voltage source is connected, in an A.C. circuit whose maximum value is 170 volt. The value of potential at a phase angle of 45º will be – (A) 120.56 Volt (B) 110.12 Volt (C) 240 Volt (D) Zero

Q.3

In an ac circuit, the current is given by i = 4 sin (100t + 30º) ampere. The current becomes maximum first time (after t = 0) at t equal to – (A) (1/200) sec (B) (1/300) sec (C) (1/50) sec (D) None of the above

Q.10

If instantaneous value of current is  = 10 sin (314 t) A, then the average current for the half cycle will be – (A) 10 A (B) 7.07 A (C) 6.37 A (D) 3.53 A

Q.4

The instantaneous value of current in an ac circuit is  = 2 sin (100t + /3) A. The current at the beginning (t = 0) will be –

Q.11

The r.m.s. value of alternating current is 10 Amp having frequency of 50Hz. The time taken by the current to increase from zero to maximum and the maximum value of current will be – (A) 2 × 10–2 sec. and 14.14 Amp (B) 1 × 10–2 sec. and 7.07 amp. (C) 5 × 10–3 sec. and 7.07 amp (D) 5 × 10–3 sec. and 14.14 Amp.

Q.12

n a circuit an a.c. current and a d, c. current are supplied together. The expression of the instantaneous current is given as i = 3 + 6 sin t Then the rms value of the current is – (A) 3 (B) 6

(A) 2 3 A (C) Q.5

(B)

3 A 2

In A.C. circuit the average value per cycle of e.m.f. or current is – (B) 0 (D) None of the above

The form factor for sinusoidal potential is – (A)  2 (C)

Q.7

3A

(D) Zero

(A) peak value / 2 (C) peak value Q.6

to an A.C. source of 200V and 50 cycle see the value of average potential difference across the mixer will be (A) 308 V (B) 264 V (C) 220 V (D) 0

 2 2

(B) 2 2 

 (D) 2

The r.m.s. value of potential due to superposition of given two alternating potentials E1 = E0 sin t and E2 = E0 cos t will be – (A) E0 (B) 2E0 (C) E0 2

(D) 0

ALTERNATING CURRENT

(C) 3 2 Q.13

(D) 3 3

The emf and the current in a circuit are – E = 12 sin (100t) ; = 4 sin (100t + / 3) then – (A) The current leads the emf by 60º (B) The current lags the emf by 60º (C) The emf leads the current by 60º (D) The phase difference between the current and the emf is zero 1

Q.14

The direction of alternating currenting current get changed in one cycle – (A) two times (B) one time (C) 50 times (D) 60 times

Q.15

If the frequency of alternating potential is 50Hz then the direction of potential, changes in one second by – (A) 50 times (B) 100 times (C) 200 times (D) 500 times

Q.16

The time period of of alternating current with frequency of one KHz one second will be – (A) 0.10 (B) 0.01 –3 (C) 1 × 10 (D) 1 × 10–2

Q.17

The value of alternating e.m.f. is e = 500 sin 100t , then the frequency of this potential in Hz is – (A) 25 (B) 50 (C) 75 (D) 100

Q.18

Q.19

The frequency of an alternating current is 50Hz, then the time to complete one cycle for current vector will be– (A) 20 ms (B) 50 ms (C) 100 ms (D) 1 s In the above question, time taken by current to rise from zero to maximum is – 1 sec 200 1 (C) sec 50

(A)

Q.20

 2  (C) rms, 2

Q.21

If the frequency of ac is 60 Hz the time difference corresponding to a phase difference of 60º is – (A) 60 s (B) 1 s (C) 1/60 s (D) 1/360 s

Q.23

The domestic power supply is at 220 volt. The amplitude of emf will be – (A) 220 V (B) 110 V (C) 311 V (D) None of this

Q.24

The phase difference between the current and the electromotive force in an ac circuit is /4 radian. If the frequency is 50 Hz, then the time difference corresponding to this phase difference, will be – (A) 0.25 s (B) 0.02 s (C) 2.5 ms (D) 25 ms

Q.25

In A.C. circuit the ratio of virtual current and the r.m.s. current is – (A) 0 (B) 0.5 (C) 1

Q.26

Q.27

(C) Q.28

(B) Irms./ 2 (D) 2 Irms.

2 I0 

I0 2

(B)

I0 

(D) 0

Sinusoidal peak potential is 200 volt with frequency 50Hz. It is represented by the equation – (A) E = 200 sin 50t (B) E = 200 sin 314t (C) E = 200 2 sin 50t (D) E =200 2 sin 314t

(D) 0, 

ALTERNATING CURRENT

2

The average value or alternating current for half cycle in terms of I0 is (A)

I0  , 2 2

The sinusoidal voltage wave changes from 0 to maximum value of 100 volt. The voltage when the phase angle is 30º will be – (A) 70.7 volt (B) 50 volt (C) 109 volt (D) – 100 volt

2 I rms./2

(C) 2 2 I rms.

1 sec 100 1 (D) sec 400

(B)

(D)

If the r.m.s. value of A.C. is Irms then peak to peak value is – (A)

(B)

In the equation fo A.C.  = 0 sin t, the current amplitude and f requency will respectively be – (A) 0 ,

Q.22

Q.29

If the instantaneous value of currents is I = 100 sin 314t Amp. then the average of current n Ampere for half cycle is – (A) 100 (B) 70.7 (C) 63.7 (D) 35.3 2

Q.30

The equation of current in an ac circuit is  = 4 sin (100t + /6) ampere. The current at the beginning (t = 0) will be – (A) 1 A (B) 2 A (C) 3 A (D) 4 A

Q.31

RMS value of ac i = i1 cos t + i2 sin t will be – (A) (C)

Q.32

1 2

1 2

(i1 + i2)

(B)

(i12 + i 22)½

(D)

 3  (C) 2 Questions based on

Q.34

2

(i1 + i2)2

(B) 70 (D) 40

Q.37

n an L.C.R series circuit R = 1, XL = 1000 and XC = 1000. A source of 100 m.volt is connected in the circuit the current in the circuit is – (A) 100 m.Amp (B) 1 .Amp (C) 0.1 .Amp (D) 10 .Amp

Q.38

Which of the following figure showing the phase relationship is correct phase diagram for an R–C circuit-

1 (i 2 + i 22)½ 2 1

The phase difference between the alternating current and voltage represented by the following equation  = 0 sin t, E = E0 cos (t +  / 3), will be – (A)

Q.33

1

(A) 190 (C) 50

4 3 5 (D) 6

(B)

I (A) V

(B)

(C)

(D)

AC circuits s

The inductance of a resistance less coil is 0.5 henry. In the coil the value of A.C. is 0.2 Amp whose f requency is 50Hz. The reactance of circuit is (A) 15.7  (B) 157 (C) 1.57 (D) 757 The inductive reactance of a coil is 1000. If its self inductance and frequency both are increased two times then inductive reactance will be – (A) 1000 (B) 2000 (C) 4000 (D) 16000

Q.35

n an L-C-R series circuit R = 10, XL = 8 and XC = 6the total impedance of the circuit is – (A) 10.2 (B) 17.2 (C) 10 (D) None of the above

Q.36

n the given figure, the potential difference is shown on R, L and C. The e.m.f. of source in volt is – ALTERNATING CURRENT

Q.39

A coil of inductance 0.1 H is connected to an alternating voltage generator of voltage E = 100 sin (100t) volt. The current flowing through the coil will be – (A)  = 10 2 sin (100t) A (B)  = 10 2 cos (100t) A (C)  = – 10 sin (100t) A (D)  = – 10 cos (100t) A

Q.40

The vector diagram of the current and voltage in a given circuit is shown in the figure. The components of the circuit will be –

(A) L–C–R (C) L–C–R or L–R

(B) L–R (D) C–R 3

Q.41

Figure shows the variation of voltage with time for an ac  = 0 sin t flowing through a circuit –

Q.46

The reactance of a capacitor is X1 for frequency n1 and X2 for frequency n2 then X1 : X2 is (A) 1 : 1 (C) n2 : n1

Q.47 (A) (B) (C) (D)

Curve P is for R–L and Q for R–C circuit Curve P is for R–C and Q for R–L circuit Both are for R–C circuit Both are for R–L circuit The power factor of the following circuit will be –

(A) 0.2 Q.43

Q.44

(B) 0.4

(C) 0.6

In a circuit, the reactance of a coil is 20 . If the inductance of the coil is 50mH then angular frequency of the current will be – (A) 400 rad/sec. (B) 1 rad/sec (C) 2.5 rad/sec (D) 0.2 rad/sec If a capacitor is connected to two different A.C. generatiors then the value of capacitive reactance is –

Q.49

(B)

(C)

(D)

Alternating current lead the applied e.m.f. by /2 when the circuit consists of –

n pure capacitive circuit if the frequency of A.C. is doubled, then the value of capacitive reactance will become – 1 times 2 1 (D) times 4

(B)

Q.50

n an A.C. circuit, a capacitor of 1F value is connected to a source of frequency 1000 rad/sec. The value of capacitive reactance will be – (A) 10 (B) 100 (C) 1000 (D) 10,000

Q.51

n an A.C. circuit capacitance of 5F has a

(D) inversely proportional to the square of frequency

ALTERNATING CURRENT

(A)

(C) No change

(C) independent of frequency

(C) only an inductance coil (D) capacitor and resistance both

n pure inductive circuit, the curves between frequency f and inductive reactance 1/XL is –

(A) Two times

(B) inversely proportional to frequency

(A) only resistance (B) only capacitor

(B) 300 (D) 600

(D) 0.8

(A) directly proportion to frequency

Q.45

A coil has reactance of 100 when frequency is 50Hz. If the frequency becomes 150Hz, then the reactance will be – (A) 100 (C) 450

Q.48 Q.42

(B) n1 : n2 (D) n12 : n22

reactance as

1 . The frequency of A.C. 1000

in MHz will be – (A) 1000/ (C) 200

(B) 100/ (D) 5000 4

Q.52

n an A.C. circuit XL = 300, XC = 200and R = 100 the impedance of circuit is – (A) 600 (B) 200 (C) 141 (D) None of the above

Q.53

A resistance of 50, an inductance of 20/ henry and a capacitor of 5/ F are connected in series with an A.C. source of 230 volt and 50Hz. The impedance of circuit is – (A) 5 (B) 50 (C) 5K (D) 500

Q.54

n an L–C–R series circuit R =

5 , XL = 9 and XC = 7. If applied voltage in the circuit is 50 volt then impedance of the circuit in ohm then impedance of the circuit in ohm will be – (A) 2 (B) 3 (C) 2 5

Q.55

2 VR

The impedance of the given circuit will be –

(A) 50 ohm (C) 200 ohm Q.61

(B) 150 ohm (D) 250 ohm

The impedance of the given circuit will be –

(A) Zero (C) 55 ohm

(B) VR (D) 5VR

Q.62

n an A.C. circuit the impedance is Z = 100 30º, then the resistance of the circuit in ohm will be – (A) 50 (B) 100 (C) 50 3

Q.58

Q.60

(D) 3 5

(C) VR/ 2

Q.57

The percentage increase in the impedance of an ac circuit, when its power factor changes form 0.866 to 0.5 is (Resistance constant) – (A) 73.2% (B) 86.6% (C) 90.8% (D) 66.6%

The potential difference between the ends of a resistance R is VR between the ends of capacitor is VC = 2VR and between the ends of inductance is VL = 3VR, then the alternating potential of the source in terms of VR will be – (A)

Q.56

Q.59

(B) Infinite (D) 2500 ohm

If E0 = 200 volt, R = 25 ohm. L = 0.1 H and C = 10–5 F and the frequency is variable, then the current at f = 0 and f =  will be respecitvely –

(D) 100 3

n an LCR circuit, the voltages across the components are VL, VC and VR respectively. The voltage of source will be – (A) [VR + VL + VC] (B) [VR2 + VL2 + VC2]1/2 (C) [VR2 + (VL + VC)2]1/2 (D) [VR2 + (VL – VC)2]1/2

Q.63

(A) 0 A, 8 A (B) 8 A, 0 A (C) 8 A, 8 A (D) 0 A. 0 A The impedance of the circuit given will be –

n an electric circuit the applied alternating emf is given by E = 100 sin (314 t) volt, and current flowing  = sin (314t +  / 3). Then the impedance of the circuit is (in ohm) – (A) 100 / (C) 100 2

2

(B) 100 (D) None of the above

ALTERNATING CURRENT

(A) Zero (C) 110 ohm

(B) Infinite (D) 90 ohm 5

Q.64

A coil of resistance R and inductance L is connected to a cell of emf E volt. The current flowing through the coil will be – (A) E/R (B) E/L

E (C) Q.65

2

L R

Q.69

n a series resonant L–C–R circuit, if L is increased by 25% and C is decreased by 20%, then the resonant frequency will – (A) Increase by 10% (B) Decrease by 10% (C) Remain unchanged (D) Increase by 2.5%

Q.70

If R = 100  then the value of X and  in the given circuit will be –

EL 2

(D)

L2  R 2

n a certain circuit E = 200 cos (314t) and  = sin (314t + /4). Thei r v ector representation is – (A)

(A) 800 V, 2A (C) 220 V. 2.2A

(B) 300 V. 2A (D) 100 V, 2A

(B) Q.71

n question (70) the value of inductance will be – (A) 0.12 H (B) 0.24 H (C) 0.31 H (D) 0.43 H

Q.72

n an LCR. series circuit the resonating frequency can be decreased by – (A) Decreasing the value of C. (B) Decreasing the value of L (C) Decreasing both the values of L and C (D) Increasing the value of C

Q.73

Which of the following statements is correct for L–C–R series combination in the condition of resonance – (A) Resistance is zero (B) Impedance is zero (C) Reactance is zero (D) Resistance, impedance and reactance all are zero

Q.74

n an LCR circuit, the resonating frequency is 500 k.Hz. If the value of L is increased two 1 times and value of C is decreased times, 8 then the new resonating frequency in kHz will be –

(C)

(D)

Q.66

n question (65) reactance X will be – (A) 70.7 ohm (C) 100 ohm

Q.67

n question (65) the power factor is – (A) 0.5 (B) 0.707 (C) 0.85 (D) 1.0

Questions based on

Q.68

(B) 0.707 ohm (D) 141 ohm

Resonance

The electric resonance is sharp in L-C-R circuit if in the circuit – (A) R is greater (B) R is smaller (C) R = XL or XC (D) Does not depend on R ALTERNATING CURRENT

(A) 250 (C) 1000

(B) 500 (D) 2000 6

Q.75

n resonating circuit value of inductance and capacitance is 0.1H and 200 F. For same resonating frequency if value of inductance is 100H then necessary value of capacitance in F will be – (A) 4 (C) 2

Q.76

(B) 0.2 (D) 0.3

n an ac circuit emf and current are E = 5 cos t volt and  = 2 sin t ampere respectively. The average power dissipated in this circuit will be – (A) 10 W (B) 2.5 W (C) 5 W (D) Zero

Q.81

The equations of alternating e.m.f. and current in an A.C. circuit are E = 5 cos t volt and = 2 sin t ampere respectively. The average power loss in this circuit will be – (A) 1 watt (B) 2.5 watt

The inductance of the motor of a fan is 1.0 H. To run the fan at 50 Hz the capacitance of the capacitor that will cancel its inductive reactance, will be – (A) 10 F (C) 0.4 F

Q.77

Q.80

(B) 40 F (D) 0.04 F

(C) 3 watt Q.82

n ac circuit at resonance : (A) Impedance = R 1    (B) Impedance =  L  C  

(C)

(D) The phase difference of current in C relative to source voltage is  Q.78

Q.85

A choke coil of 100 ohm and 1 H is connected to a generator of E = 200 sin (100t) volt. The average power dissipated will be – (A) Zero (B) 200 W (C) 141 W (D) 100 W

Q.86

A choke coil of negligible resistance carries 5 mA current when it is operated at 220 V. The loss of power in the choke coil is – (A) Zero (B) 11 W (C) 44 × 103 W (D) 1.1 W

Power

(A) 600 W

(B) 500 W

(C) 400 W

(D) 200 W

ALTERNATING CURRENT

5

n an ac circuit the readings of an ammeter and a voltmeter are 10 A and 25 volt respectively, the power in the circuit will be – (A) More than 250 W (B) Always less than 250 W (C) 250 W (D) Less than 250 W or 250 W

(D) Impedance will increase and become capacitive

n an ac circuit 6 ohm resistor, an inductor of 4 ohm and a capacitor of 12 ohm are connected n series with an ac source of 100 volt (rms). The average power dissipated in the circuit will be –

(D)

2 1

Q.84

(C) Impedance will increase and become inductive

Q.79

3

1

(B)

n an L–C–R series circuit the loss of power is in – (A) Only R (B) Only L (C) Only C (D) both L and C

(B) Impedance will remain remain unchanged

Questions based on

1 2 1

Q.83 An ac circuit resonates at a frequency of 10 kHz. If its frequency is increased to 11 kHz, then : (A) Impedance will increase by 1.1 times

The series combination of resistance R and inductance L is connected to an alternating source of e.m.f. e = 311 sin (100 t). If the value of wattless current is 0.5A and the impedance of the circuit is 311, the power factor will be – (A)

(C) The voltages across L and C are in the same phase

(D) Zero

7

Q.87

The ratio of apparent power and average power in an A.C. circuit is equal to –

Q.93

If a bulb and a coil are connected in series with D.C. source and a iron core put in the coil then the glowing of bulb – (A) Decreases (B) Increases (C) No change (D) Zero

Q.94

Three bulbs of 40, 60 and 100 watt are connected in series with the source of 200 volt. Then which of the bult will be glowing the most – (A) 100 watt (B) 60 watt (C) 40 watt (D) All are glowing equally

Q.95

If two bulbs each of 220V, 30 watt are connected in series, then we get electric power as – (A) 60 watt (B) 15 watt (C) 6 watt (D) 30 watt

Q.96

Two electric bulbs of 100 watt (220 volt) are connected in series and these are connected with other bulb of 100W (220V) in parallel then total power in watt will be –

(A) Reciprocal of power factor (B) Efficiency (C) Power factor (D) Form factor Q.88

n an A.C. circuit, a resistance of 3, an inductance coil of 4and a condenser of 8 are connected in series with an A.C. source of 50 volt (R.M.S.). The average power loss in the circuit will be (A) 600 watt (C) 400 watt

Q.89

 ) 2 ampere an A,V, V = 200 sin (100 t) volt. The power loss in the circuit will be –

In an A.C. circuit, i = 5 sin (100t–

(A) 20 volt (C) 1000 watt

Questions based on

Q.90

Q.92

(B) 40 volt (D) 0 watt

Bulbs & AC meter

When N identical bulbs are connected in parallel, total power consuption is P, what would be the power consuption when they connected in series(A) P (C) P/N

Q.91

(B) 500 watt (D) 300 watt

(B) PN (D) P/N2

Two bulbs of 500 watt and 300 watt work on 200 volt r.m.s. the ratio of their resistances will be – (A) 25 : 9

(B) 3 : 5

(C) 9 : 25

(D) 5 : 9

An air core coil and an electric bulb are connected in series with an A.C. source. If an iron rod is put in the coil, then the intensity of bulb’s will – (A) Be same (B) Increase (C) Decrease

(A) 300 watt (C) 150 watt Q.97

(B) 50 watt (D) 25 watt

The A.C. meters are based on the principle of – (A) Heating effect (B) magnetic effect (C) Chemical effect (D) Electromagnetic effect

(D) Decrease, increase ALTERNATING CURRENT

8

Q.98

The correctly marked ammeter for A.C. current is shown in (A)

Q.100 The A.C. meters measure its – (A) root mean square value (B) peak value (C) square mean value (D) None of the above

(B)

0 1

2

3

(C) (D) None of these Q.99

Alternating current can not be measured by direct current meters, because – (A) alternating current can not pass through an ammeter (B) the average value of current for complete cycle is zero (C) some amount of alternating current is destroyed in the ammeter. (D) None of these

ALTERNATING CURRENT

9

LEVEL # 2 Q.1

The self inductance of a choke coil is 10mH. When it is connected with a 10V D.C. source, then the loss of power is 20 watt. When it is connected with 10 vott A.C. source loss of power is 10 watt. The frequency of A.C. source will be – (A) 50Hz (C) 80Hz

Q.2

(B) 60Hz (D) 100Hz

We have two cables of copper of same length. In one, only one wire of corss–section area A and in second ten wires each of cross– section area A/10 are present. When A.C. and D.C. flow in it. Choose the correct cable for better efficiency –

(A) Same in both (B) More in B1 (C) Depending on the frequency of the source (D) More in B2 Q.6

An L–C–R series circuit with a resistance of 100 ohm is connected to an ac source of 200 V (rms) and angular frequecncy 300 rad/s. When only the capacitor is removed. the current lags behind the voltage by 60º. When only the inductor is removed , the current leads with the voltage by 60º. The average power dissipated is – (A) 50W (B) 100 W (C) 200 W (D) 400 W

Q.7

A coil when connected to a dc source of 12 V, carries a current of 4 A. If this coil is connected to an ac source of 12 V and 50 rad/s, then it carries a current of 2.4 A. The inductance of the coil is – (A) 48 H (B) 4 H (C) 12.5 H (D) 8 × 10–2 H

Q.8

Waves of wavelength 300 m are transmitted from a broadcasting station. If a capacitor f 2.4 F is used in a resonant circuit for these waves, then the inductance of coil used will be – (A) 10–6 H (B) 1.056 × 10–8 H –8 (C) 10.56 × 10 H (D) 105.6 × 10–8 H

Q.9

A generator of 100 V (rms) is connected in an ac circuit and 1 A (rms) current is flowing in the circuit. If the phase difference between the voltage and the current is /3. then the average power consumption and the power factor of the circuit will be – (A) 50 W, 0.86 (B) 100 W, 0.86 (C) 100 W, 0.5 (D) 50 W, 0.5

(A) Only one wire for D.C. and the other for A.C (B) Only one wire for A.C. and the other for D.C. (C) Any wire for D.C. but only multy–wire cable for A.C. (D) Only one wire for D.C. and only multy–wire packet for A.C. Q.3

n a series LCR circuit L = 1H, C = 6.25 F and R = 1 ohm. Its quality factor is – (A) 400 (C) 125

Q.4

(B) 200 (D) 25

A bulb of rated values 60 V and 10 W is connected in series with a source of 100 V and 50 Hz. The coeficient of self induction of a coil to be connected in series for its operation will be – (A) 1.53 H (B) 2.15 H (C) 3.27 H (D) 3.89 H

Q.5

Two identical bulbs B1 and B2 are connected to an ac source. B is connected in series with a coil of 100 mH and B2 with a capacitor of 10 F as shown in the figure. The brightness of B1 and B2 will be– ALTERNATING CURRENT

10

Q.10

When a current of 0.5 A (rms) is passed through a coil, its reactance and power loss are found to be 25 ohm and 16 W. The impedance of the coil is – (A) 50 ohm (C) 76.4 ohm

Q.11

(B) V2 (D) V4

(B) V1 and V3 (D) V1 and V2

(A) (B) (C) (D)

n ac circuit contains a pure capacitor, across which an ac emf e = 100 sin (1000t), volt is applied. If the peak value of the current is 200 mA, then the value of the capacitor is – (A) 2 F (B) 20 F (C) 5 F (D) 500F

Q.19

n a series LCR circuit C = 25 F, L = 0.1 H and R = 25. When an ac source of emf e = 311 sin (314t) then the impedance is – (A) 99 ohm (B) 80 ohm (C) 57 ohm (D) 25 ohm

Q.20

Consider two cables A and B. n A, a single copper wire of cross–sectional area x is used, while in B, a bunch of 15 wires each of cross– sectional area x/15 is used. Then for the flow of high frequency AC, the – (A) Cable A is more suitable then B (B) Cable B is more suitable then A (C) Both cables are equally suitable (D) Nothing specific can be predicted

(B) 0.06, 0.6W (D) 4.8, 0.6W.

The current through 'a' wire changes with time according to the equation I =

t . The

correct value of the rms current within the time interval t = 2 to t = 4s will be – (A)

3 A

(B) 3 A (C) 3

3 A (D) None of the above ALTERNATING CURRENT

There must be a capacitor in the box There must be an inductor in the box There must be a resistance in the box The power factor is 0.707

Q.18

(B) 100 volt (D) uncertain

2.5/ F capacitor and a 3000–ohm resistance are joined in series to an a.c. source of 200 volt and 50 sec–1 frequency. The power factor of the circuit and the power dissipated in it will respectively– (A) 0.6, 0.06W (C) 0.6, 4.8W

Q.15

Figure 92 shows an AC generator connected to a “block box” through a pair of terminals. The box contains possible R,L, C or their combination, whose elements and arrangements are not known to us. Measurements outside the box reveals that e = 75 sin ( t) volt, i = 1.5 sin (t + 45º) amp then, the wrong statement is –

n Q.11, if L /R = 10 and V3 = 100 volt then reading of V2 will be – (A) 10 volt (C) 1000 volt

Q.14

Q.17

n the above problem, the two voltmeters whose readings are equal, will be – (A) V4 and V1 (C) V4 and V5

Q.13

The time required for a 50Hz alternating current to increase from zero to 70.7% of its peak value is – (A) 2.5 ms (B) 10 ms (C) 20 ms (D) 14.14 ms

n the adjoining A.C. circuit the voltmeter whose reading will be zero at resonance is –

(A) V1 (C) V3 Q.12

(B) 68.7 ohm (D) 92.3 ohm

Q.16

11

Q.21

An ac circuit contains a resistance R and a reactance X. If the impedace of the circuit is given by Z = 50  / 6 Then the resistance and the reactance are, respectively (in ohms) –

Q.23

A d.c. voltage with appreciable riple expressed as V = V1 + V2 cos t is applied to a resistor R. The amount of heat generated per second is given by (A)

V12  V22 2R

(B)

(C)

V12  2V22 2R

(D) None of these

(A) Zero ; 50 (B) 25 3 ; 25

2 V12  V22 2R

(C) 25 ; 25 3 (D) 25 ; 25 Q.22

n a series LCR circuit with R = 11 ohm, the instantaneous value of the current i in the circuit and instantaneous value of the appled ac emf e, are respecitvely – i = 200 mA, e = 110 volt If the phase difference between the current and voltage is /3, then the instantaneous ac power in the circuit is – (A) 22W (C) 0.22W

(B) 0.44W (D) None of the above

ALTERNATING CURRENT

12

LEVEL # 3 Q.1

The electric current in a circuit is given by i t i  0 for some time. The rms current for  the period t = 0 to t =  will be-

(A)

Q.2

i0 2

(B)

i0 3

(C)

i0 2

(D)

i0 3

Q.6

A series AC circuit has a resistance of 4 and an inductor of reactance 3. The impedance of

Q.3

(D) 2 : 1

An AC source is rated 220 V, 50 Hz. The average voltage is calculated in a time interval of 0.01 s, It (A) must be zero

(C) R, R

(D) 2R, R 3

In a series LCR circuit the voltage across the resistance, capacitance and inductance is 10 V each. If the capacitor is removed, the voltage across the inductance will be-

(C)

Q.7 (C) 4 : 5

(B) 2R, R 2

(A) 10 V

the circuit is z1. Now a capacitor of reactance 6 is connected in the series of above combination, the impedance becomes z2 , Then z1 will bez2 (A) 1 : 1 (B) 5 : 4

(A) R, R 2

10

(B) 10 2 V

V

(D) 20 V

2

An alternating emf 100 cos 100 t volt is connected in series to a resistance of 10  and inductance 100 mH, what is the phase difference between the current in the circuit and the emf(A)

 4

(B) zero

(B) may be zero (C) 

(C) is never zero

(D) is

20

Q.5

An AC ammeter is used to measure current in a circuit. When a given direct current passes through the circuit, the AC ammeter reads 3A. When another alternating current passes through the circuit the AC ammeter reads 4 A, then reading of this ammeter if DC and AC f low through the circuit simultaneously is(A) 3 A

(B) 4 A

(C) 7 A

(D) 5 A.

 2

volt .

2

Q.4

(D)

An inductor (L) and resistance (R) are connected in series with an AC source. The phase difference between voltage (V) and

Q.8

1 A coil having an inductance of henery is  connected in series with a resistance of 300  If 20 V from a 200 cycle/s source are impressed across the combination. The power factor of the circuit will be-

(A)

Q.9

2 5

(B)

3 5

(C)

4 5

(D)

In an AC circuit, a resistance of R ohm is connected in series with an inductance L. If phase angle between voltage and current be 45°, the value of inductive reactance will be(A) R/4

current (i) is 45°. Now a capacitor (C) is connected in series with L-R, If the phase

(B) R/2

difference between V and i remain same, then capacitive reactance and impedance of L-C-R circuit will be-

(D) Cannot be found with the given data

ALTERNATING CURRENT

2 3

(C) R

13

Q.10

In LCR series AC circuit, the phase angle between current and voltage is-

Q.16

(A) any angle between 0 and ±/ 2

In an AC circuit, the current lags behind the voltage by /3. The components of the circuit are-

(B) / 2

(A) R and L

(B) L and C

(C) 

(C) R and C

(D) only R

(D) any angle between 0 and  Q.17 Q.11

Q.12

Q.13

Q.14

A 10 ohm resistance, 5 mH coil and 10 F

A coil has an inductance of 0.7 H and is joined in series with a resistance of 220 . When an alternating e.m.f. of 220 V at 50 cps is applied to it, then the wattless component of the current in the circuit is-

capacitor are joined in series. When a suitable

(A) 5 ampere

(B) 0.5 ampere

frequency-

(C) 0.7 ampere

(D) 7 ampere

(A) is halved

frequency alternating current source is joined to the combination the circuit resonates. If the resistance is halved, the resonance

(B) is doubled

A direct current of 2 A and an alternating current having a maximum value of 2 A flow through two identical resistances. The ratio of heat produced in the two resistances will be(A) 1 : 1

(B) 1 :2

(C) 2 : 1

(D) 4 : 1

(C) remains unchanged (D) is quadrupled Q.18

An alternating voltage is connected in series with a resistance R and an inductance L. If the potential drop across the resistance is 200 volt and across the inductance is 150 volt, the applied voltage is(A) 350 volt

(B) 250 volt

(C) 500 volt

(D) 300 volt

I = I0 sin t is passed through the wire AB, the wire willA

N I

An AC circuit using an inductor and a capacitor in series has a maximum current. If L = 0.5 H and C = 8 F, then the angular frequency of input AC voltage will be (A) 500

(B) 5 × 105

(C) 4000

(D) 5000

A conducting wire is stretched between the poles of a magnet. There is a strong uniform magnetic field in the region between the poles. If an alternating current

S

B (A) remain stationary (B) be pulled towards north pole (C) be pulled towards south pole (D) vibrate with a frequency /2

Q.15

A resistor and an inductor are connected to an AC supply of 120 volt and 50 Hz. The current in the circuit is 3 ampere. If the power consumed in the circuit is 108 watt, then the resistance in the circuit is-

Q.19

In an LR circuit, the inductive reactance is equal to resistance R of the circuit. An e.m.f. E = E0 cos t is applied to the circuit. The power consumed in the circuit is-

(A) 12 ohm

(B) 40 ohm

(A) E 20 / R

(B) E02 / 2R

(C)

(D) 360 ohm

(C) E02 / 4R

(D) E02 / 8R

(52  28 ) ohm

ALTERNATING CURRENT

14

Q.20

The voltage of an AC supply varies with time (t) as V = 120 sin 100 t cos 100t. The maximum voltage and frequency respectively are (A) 60 volt, 100 Hz (C) 120 volt, 100 Hz

(B)

Q.21

Statement II : At this frequency, inductive reactance is equal to capacitative reactance.

120

volt, 100 Hz 2 (D) 60 volt, 200 Hz

Q.22

Statements type question : Each of the questions given below consist of Statement – I and Statement – II. Use the following Key to choose the appropriate answer.

Statement I : In series LCR circuit , the resonance occurs at one frequency only.

Statement I : A glowing bulb becomes dim when an iron bar is put in the inductor in the a.c. circuit. Statement II : Resistance of the circuit increases.

Q.23

Statement I : A capacitor blocks d.c. Statement II : This is because capacitative 1 1 reactance of condenser is XC = = and C 2fC for d.c. f = 0.

(A) If both Statement- I and Statement- II are true, and Statement - II is the correct explanation of Statement– I. (B) If both Statement - I and Statement - II are true but Statement - II is not the correct explanation of Statement – I.

Q.24

(C) If Statement - I is true but Statement - II is false.

Statement I : In 220 V ; 50 Hz a.c. wall plug peak value of alternating emf is 220 V. Statement II : Only rms value is specified.

Q.25

Statement I : Series RLC circuit behaves as RC circuit for f < fr .

(D) If Statement - I is false but Statement - II is true.

ALTERNATING CURRENT

Statement II : Because for f < fr capacitative reactance is more than inductive reactance.

15

LEVEL # 4 ( Question Q.1

SECTION - A The power factor of an A.C. circuit having resistance (R) and inductance (L) connected in series and an angular velocity  is – [AIEEE-2002]

Q.3

(B)

L R

(D)

R R2   2L2

The phase difference between the alternating current and emf is /2. Which of the following cannot be the constituent of the circuit ? [AIEEE-2005] (A) C alone (B) R L (C) L C (D) L alone

Q.10

In a series resonant LCR circuit, the voltage across R is 100 volts and R = 1 k with C = 2 F. The resonant frequency  is 200 rad/s. At resonance the voltage across L is – [AIEEE 2006] (A) 250 V (B) 4 × 10–3 V (C) 2.5 × 10–2 V (D) 40 V

Q.11

In an a.c. circuit the voltage applied is E = E0 sint. The resulting current in the

R  L

(D) none of these

Alternating current can not be measured by D.C. ammeter because – [AIEEE-2004]

(D) 0 V (zero)

Q.9

2 2

The core of any transformer is laminated so as to – [AIEEE-2003] (A) Make it light weight (B) Make it robust and strong (C) Increase the secondary voltage (D) Reduce the energy loss due to eddy current

(C) 100 V

A circuit has a resistance of 12 ohm and an impedance of 15 ohm. The power factor of the circuit will be – [AIEEE-2005] (A) 0.8 (B) 0.4 (C) 1.25 (D) 0.125

(R   2 L2 )1/ 2

2

(B) 50 2

Q.8

2

R

(B)

(A) 50 V

In a LCR circuit capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to – [AIEEE-2004] (A) 4 L (B) 2 L (C) L/2 (D) L/4

R

R L

In an LCR series a.c. circuit, the voltage across each of the components, L, C and R is 50 V. The voltage across the LC combination will be – [AIEEE-2004]

Q.7

Power factor of the circuit is –[AIEEE-2003]

(C)

Q.5

(R 2   2 L2 )1/ 2

In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If current in primary is 4 A, then that in the secondary is – [AIEEE-2002] (A) 4 A (B) 2 A (C) 6 A (D) 10 A

(A)

Q.4

Q.6

R

R (A) L

(C)

Q.2

asked in previous AIEEE & IIT-JEE)

 

circuit is I = I 0 sin  t 

  . The power 2

consumption in the circuit is given by [AIEEE 2007]

(A) A.C. can not pass through D.C. Ammeter (B) A.C. changes direction

(A) P =

E0I0 2

(B) P = zero

(C) Average value of current for complete cycle is zero

(C) P =

E 0I0 2

(D) P =

(D) D.C. Ammeter will get damaged ALTERNATING CURRENT

2 E 0I 0

16

Q.1

SECTION - B In an AC circuit phase difference between current and potential is /4. The variation of I & E Vs t is represented in the graph. If E = E0 cos (100 t) , then components of the circuit are – [IIT 2003]

(A) R=100, C=1µF (B) R=1k, C=10µF (C) R=100; L=1H (D) R=1k; L=10H

ALTERNATING CURRENT

17

ANSWER KEY

LEVEL

# 1

Q. No.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Ans.

D

A

B

B

B

C

A

D

D

C

D

D

A

A

B

C

B

A

A

A

Q. No.

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

Ans.

B

D

C

C

C

C

A

B

C

B

C

D

B

C

A

C

A

D

D

C

Q. No.

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Ans.

A

D

A

B

B

C

B

C

B

C

B

C

B

B

A

C

D

B

A

D

Q. No.

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

Ans.

B

D

B

A

A

D

B

B

C

C

D

D

C

C

B

A

A

C

A

D

Q. No.

81

82

83

84

85

Ans.

D

B

A

D

D

86 A

87 A

88 D

89 D

90 D

91 B

92 C

93 C

94 C

95 B

96 C

97 A

98 B

99 B

100 A

13 C

14 C

15 A

16 A

17 B

18 A

19 A

20 B

LEVEL Q. No. Ans. Q. No. Ans.

1 C

2 C

3 A

21 B

22 A

23 B

4 A

5 C

6 D

7 D

8 B

9 D

# 2

10 B

11 D

LEVEL

12 D

# 3

Que s.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

Ans.

B

A

B

D

B

C

A

B

C

A

B

C

B

A

A

A

C

D

C

Que s.

20

21

22

23

24

25

Ans.

A

A

C

A

D

A

LEVEL

# 4

SECTION-A Q. No. Ans.

1 B

2 B

3 B

4 D

5 C

6 D

7 C

8 A

9 B

10 A

11 B

SECTION-B Q. No. Ans. ALTERNATING CURRENT

1 B 18