1. Effective voltage is given by expression

Transcription

1 Chapter 07 A C CIRCUITS

2 1. Effective voltage is given by expression 1) Ve = Vo/ 2 2) Ve = 2 Vo 3) Vo/π 4) π Vo Effective voltage isrms voltage Answer is (1)

3 2. A coil having zero resistance is connected in series with a 90Ω resistance and the combination i is connected to 120V, 60 Hz line. A voltmeter reads 36 V across the resistance and 114 V across the coil. The self inductance of the coil is 1) H 2) 0.76 H 3) 7.6 H 4) 76 H

4 Given V R = 36 V R = 90 Ω I = V/R =36/90 = 0.4 A Also given V L = 114V X L = V L /I 2πυL = 114/0.4 L = 114/2x3.14x60x0.4 = 0.76 H

5 3. A radio transformer has 660 turns of wire in the primary coil which is connected to 220 V AC source. The secondary coil supplies 6.3V 63V for the filament of a bulb. What is the number of turns in the secondary? 1) 2 2) 4 3) 19 4) 57

6 Ns/Np = Vs/Vp Ns = Vs Np /Vp = 6.3 x660 / 220 = 6.3x 3 =18.9 =19

7 4. A current of 4A flows in a coil when connected to a 12 V dc source. If the same coil is connected to a 12V, 50 rad s 1 ac source, acurrent of 2.4 A flows. The inductance of the coil is 1) 80 H 3) 80 mh 2) 8 H 4) 8 mh.

8 I dc = 4A V dc = 12 V R = V dc / I dc = 12 /4 =3Ω V ac = 12V, I ac = 2.4 A Z = V ac / I ac = 12 /2.4 =5Ω ω= 50 rad s 1 L = ( Z 2 R 2 ) / ω = 4/50 =0.08 = 80 mh

9 5. An a.c. having a peak value 28 A is used to heat a metal wire. To produce the same heating effect a constant tcurrent I that t can be used is 1) 28A 2) about 20A 3) 7A 4) about 10A Answer : Idc = Irms = Io / 2 = 28/1.41 =20 A

10 6. A circuit has a resistance of 30 Ω in series with an inductive reactance of 40 Ω. They are connected in series with an ac source. If the peak value of current is 1 A and the peak voltage is 220 V, the power consumed by the circuit is 1) 66 W 2) 6.6. W 3) 0.66 W 4) 33 W

11 R=30 Ω X L = 40 Ω. Z= (R 2 + X L 2 )= 50Ω P = ½ (VoIo cos φ) = ½ VoIo (R/Z) = ½ x1x 220 x0.6 = 66 W Answer is ( 1)

12 7. In the circuit shown V AB = V AC, then P is 1) an inductor 2) a capacitor 3) a suitable combination of inductor and capacitor 4) resistor

13 V BC = 0 It is possible iff X is a combination L & C at resonance

14 8. In an ac circuit, the voltage V and the current I are given by V = 100 sin ( 100 πt t ) volt and I = 100 sin ( 100t + π/3 ) ma. The power dissipated in the circuit is 1) zero 2) 10 3) 5 W 4) 2.5 W

15 P = ½(VoIo cos φ) = ½(100x100x10-3 cos 60) = ½ x10x0.5 = 2.5 W

16 9. In a series LCR circuit, it R = 100 Ω and applied ac voltage is 200 V. When the capacitance alone is removed, the voltage leads the current by When the inductance alone is removed, the voltage lags the current by Then the current in the circuit is 1) 0.5 A 2) 1 A 3) 2A 4) 4 A

17 Net phase difference between V & I φ= φ 1 + φ 2 = = 0 So ckt is in resonance I = V/R = 200/100 = 1 A

18 10.A 4 µf capacitor charged to 50 V is connected across an ideal inductor of inductance 10 mh. The maximum value of current in the circuit is 1) 20 ma 2) 2 ma 3) 1 ma 4) 1 A

19 Given, C = 4 µf V= 50 V 3 L = 10 x 10 3 H. Energy stored in the capacitor is converted into energy in the inductor ½ LI 2 = ½ CV 2 ½ x 10 x I 2 = ½ 4x x 2500 I 2 = 1 Answer is (4) = 1 A

20 11.A transformer is used to light 140 watt, 24 volt lamp from 240 V ac mains. The current in the main cable is 0.7 A. The efficiency of the transformer is 1) 63.8% 2) 84% 3) 83.3 % 4) 48%

21 Given ; Ps =140 watt, Vs=24 volt Vp = 240 V Ip= 0.7 A. The efficiency of the transformer η = Ps/Pp η = Ps/Vs Is =140/(24 x0.7) = 20/24 = Answer is (3) = %

22 12.In a LRC circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should ldbe changed from L to 1) 4L 2) 2L 3) L/2 4) L /4

23 For the resonant frequency to remain unchanged LC = const Lα1/C If C C, then L L/2 Answer is ( 3) = L/2

24 13.An ac source E = sin 100t is connected across a circuit containing a AC ammeter and a capacitor of capacity 1µ F. Then the reading of the ammeter is 1) 10mA 2) 20mA 3) 40mA 4) 80mA

25 E = sin 100t comparing with E = Eo sin ωt Eo = & ω = 100 Reading of the ammeter I = E/Xc I = Eo/ 2 Xc = 200 x ω C = 200x100 X10 6 = 2X10 2 = 20X10 3 A Answer is (2) = 20mA

26 14.The impedance of a coil of resistance R to AC of frequency 50Hz is 3R. The self inductance of the coil is (if R = 6.28Ω) 1) 0.25 H 2) 2.5 H 3) H 4) H

27 Z = 3 R υ= 50Hz &R = 6.28Ω L = ( Z 2 R 2 ) / 2πυ = ( 3R 2 R 2 ) /2πυ = 2 x R / 2πυ = 2 x6.28 /2x 3.14 x50 =1.41/50 = H Answer is (3)

28 15.The reactance offered by a coil to AC of certain frequency is equal to its resistance. The phase difference between the voltage across the coil to the current through the coil in radians is 1) π/3 2) π/6 3) π/2 4) π/4

29 Given X L =R Thephasedifference between thevoltage across the coil to the current through the coil tan φ = (X L Xc)/R =X L /R = 1 Φ = π/4/ Answer is 4) π/4

30 16.The choke coil has a resistance 8 Ω and the inductive reactance 6 Ω. The power factor of the coil is 1) ` 2) ) 0.4 4) 0.3

31 Given, R =8 Ω X L = 6 Ω. The power factor of the coil, Cos φ = R/Z =8/10 = 0.8 Answer is (2) = 0.8

32 17.An alternating current is given by I= I 1 cos wt + I 2 sin wt. the rms current is given by n

33 φ Io = (I 2 +I ) I 1 I 2 cosφ) but) φ=90 0 Io = (I 2 +I ) Irms = Io/ 2 = (I 2 +I )/2 Answer is

34 18.In the circuit shown, the inductor used is an ideal one. The current in the circuit when the switch is closed is 1) 0.2 A 2) 0.3 A 3) 1 A 4) 0.14 A

35 Since the inductor is ideal, the circuit can be written as I = E/(R e +r) I =10/10 = 1A Answer is (3) I = 1A

36 19.Reciprocal of impedance is called 1) conductance 2) admittance 3) conductivity 4) resistivity Answer is (2)

37 20.In an ac circuit the virtual power is 50 W and the power factor is ½. Then the actual power is 1) 50 W 2) 100 W 3) 25 W 4) 75 W

38 P av = VI cosφ P av = P vir cosφ P av = 50 x ½ Answer is (3) = 25 W

39 21.The primary of a transformer has 1000 turns and secondary has 2000 turns. For any input voltage, the power in the secondary is 1) double that in primary 2) less or equal to that in primary 3) half of that in primary 4) 15times 1.5 that in primary Answer is (2)

40 22.In an AC circuit containing a pure inductor and a capacitor, the current and voltage are 1) in phase 2) out of phase by ) out of phase by ) out of phase by 45 0 Answer is (1)

41 23.The band width of a resonance curve with respect to a series RLC circuit is 48 khz. If the quality factor is 3, the resonant frequency is 1) 51 khz 2) 45 khz 3) 144 khz 4) 16 khz

42 Q = υ o / BW Given, B.W = 48 khz. Q= 3 υ o = Q xbw = 3x 48 khz. = 144 khz Answer is (3) = 144 khz

43 24.An inductor of inductance 2 H and a resistance of 10 Ω are connected to a battery of 5 V in series. The initial rate of change of current is 1) 0.5 A /s 2) 1.25 A/s 3) 2.5 A/s 4) 2 A/s

44 Given : L = 2 H and a resistance of 10 Ω are connected to a battery of 5 V in series. The initial rate of change of current is Applying kirchof s loop rule to the ckt E L.(dI/dt) = IR Initially, I = 0 di/dt = E/L = 5/10= 0.5A/s Answer (1) = 0.5 A /s

45 25.A bulb B and a capacitor C are connected to a battery as shown in figure. When the switch S is closed. 1) the bulb will glow when the capacitor fully gets charged. 2) the bulb glows during charging of the capacitor. 3) the bulb will not glow at all 4) the bulb glows intermittently due to to the charging and discharging of the capacitor.

46 Bulb glows only when current flows through thecircuit circuit. In the given circuit, current flows during charging and discharging of the capacitor. When the switch S is closed, the process is charging Hence the answer is (2) = the bulb glows during charging of the capacitor

47 27.Which of the following statements is not true at the resonant frequency of a series LCR circuit. 1) inductive reactance = capacitive reactance 2) resonant frequency is independent of resistance 3) current in the circuit is minimum 4) impedance is purely resistive in nature. Answer is (3)

48 26. The inductance of a coil is 5H.What is its effective reactance in dc circuit? 1)0 2) infinity 3) 5Ω 4)0.2Ω For DC, frequency υ = 0 but X L =2πυL = 0 Answer is (1)

49 28.Power in an ac circuit depends on (A) rms value of voltage (B) rms value of current (C) phase difference between voltage and current 1) Only A is correct 2) Only B is correct 3) Both A & B are correct 4) All A,B & C are correct

50 Power in an ac circuit P = (V rms I rms cos φ) Answer is (4)

51 29.Which h of the fallowing has the dimension i of resistance R (υis the frequency of AC) 1)υC 2) =2πυL 3) C/υ 4) L/υ [ R] = [ X L ] but X L =2πυL [ R] = [υl ]

52 30. For long distance transmission, the AC is stepped up because transmission at high voltage is 1) faster 2) economical 3)not damped 4)not dangerous Transmission power loss P = I 2 R As V increases I decreases P decreases. So transmission at high voltage is economical. Answer is (2)

53 Transmission power loss P = I 2 R As V increases I decreases P decreases transmission at high voltage is economical. Answer is (2)

54 31.The transformer varies theoutput 1) Energy 2) Power 3) Frequency 4) Current Answer is (4) = current

55 32.The core of the transformer is laminated to 1) reduce eddy current 2)reduce self induction 3)increase the efficiency 4)decrease theweight ofthetransformer transformer Answer is (1)

56 33.Iron core decreases the loss of energy due to 1)heating 2) eddy currents 3)flux leakage 4)hysteresis Answer is (4)

57 34. The AC cannot be used for 1) heating 2) lighting i 3) electrolysis 4) generate mechanical energy Answer is (3)

58 35.What is the average value of ac over a complete cycle? 1)zero 2)I o / 2 3)2I o /π 4) 2I o Answer is (1)

59 36. The power factor varies between 1)zero to 0.5 2)0.5 to 1 3)zero to 1 4)1 and 2 Ans ; PF = cos φ which varies from 0 & 1

60 37.How does the current in an RC circuit vary when the charge on the capacitor builds up? 1)It increases linearly 2)It increases exponentially 3)It decreases linearly 4)It decreases exponentially Answer is (4)

61 38.The frequency of ac is 50Hz. How many timesinonesecond in second does thevoltage inthe current does becomes zero? 1)25 2)50 3)100 4)150 Answer is (3)

62 39.Why 220V ac is more dangerous than 220V dc? 1) The dc attracts 2)Peak voltage for ac is much larger 3)The body offers less resistance to ac 4) Due to some other reason Answer is (2)

63 40.What is the nature of graph between inductive reactance and frequency of ac for series RCL circuit? 1)Straight line 2)Parabola 3)Hyperbola 4)Bell shaped Answer is (1)

64 X L =2πυL It is of the form y = mx which is a Straight line passing through the origion with slope m= 2πL Answer is (1)

65 41. The impedance of a 10microfarad capacitor for 50 rad/s ac is 1)2 Ω 2) 20Ω 3) 200Ω 4) 2000Ω

66 The impedance Xc = 1/ ωc Xc = 1/ (50x10x10 66 ) =2000Ω Answer is (4)

67 42. A 1.0mH inductance a 10µF capacitance and a ac source. It is found that the inductor and the capacitor show equal resistances. The reactance should be nearest to 1)100Ω 2)32Ω 3)10Ω 4)3.2Ω

68 The circuit is in resonance. But resonant frequency ω = 1/ LC ω = 1/ 1x10-3 X10x10-6 = 10 4 X L = ω L = 10 4 x10-3 = 10 Answer is (3) =10Ω

69 43. In a circuit resistance R, capacitance C, and inductance L are in series with a sinusoidal power source. If the voltage across R, C and L are 80V, 10V and 70V respectively, then the voltage across the source terminals will be 1)100V 2)110V 3)140V 4)160V

70 V 2 = V R2 2 +(V C V L ) = (10 70) 2 = = V = 100V Answer is (1) = 100V

71 44. The inductance of a coil is 5H.What is its effective reactance in dc circuit? 1) 0 2) infinity 2) 3) 5Ω 4) 0.2Ω X L = ω L = 0xL = 0 Answer is (1)

72 45. For a choke coil the resistance is R and reactance is X. Which of the following relations is valid? 1) RX 2)R=X 3)R X 4)RX Answer is (4)

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