2. In RC circuit, charge on capacitor (when being discharged) is maximum at [BP 2013]
[BP 2013]
t=0
t=∞
t=RC
t=1/RC
(a) Charge decays exponentially as Q=Q0e-t/RC, maximum at t=0
3. A circuit has resonance frequency f. If capacitance is doubled then new frequency of circuit is:
f/√2
√2f
f/2
None
(a) Resonance frequency f = 1/(2π√(LC)), so f ∝ 1/√C → f' = f/√2 when C doubles
4. A door metal detector uses a principle based on [BP 2011]
[BP 2011]
Diffraction of sound
Alternating current and pulse
Interference
Beat frequency
(d) Metal detectors use beat frequency principle between two oscillators
5. A coil of inductance 8.4 mH and resistance 6Ω is connected to a 12V battery. The current in the coil is 1A at approx. time? [BP 2009]
[BP 2009]
500s
320ms
35ms
1ms
(d) Time constant τ = L/R = 1.4ms, using I = I0(1-e-t/τ) ≈ 1ms for I=1A (I0=2A)
6. An emf of 15 volt is applied in a circuit coil containing 5 Henry inductance and 10Ω resistance. The ratio of the current at time t=∞ and at t=1 sec is [BP 2009]
7. In LCR circuit having L=8H, C=0.5μF and R=100Ω connected in series produces natural angular frequency [MOE 2014]
[MOE 2014]
200 radian
300 radian
400 radian
500 radian
(d) ω0 = 1/√(LC) = 1/√(8×0.5×10-6) = 500 rad/s
8. The AC voltage is E=100√2 cos100t volt is connected to a capacitor of capacitance 10μF. The current flowing through the capacitor is [MOE 2014]
[MOE 2014]
10mA
100mA
1A
1000mA
(b) XC=1/(ωC)=1kΩ, I=V/XC=100mA (RMS)
9. At resonance condition the effective resistance in LCR series circuit is [2012,13]
[2012, 2013]
Maximum
Minimum
Zero
Infinity
(b) At resonance, impedance Z=R (minimum) as XL=XC
10. The average power of LCR circuit dissipated through AC circuit is: [MOE 2010]
[MOE 2010]
Im × Em
Irms × Erms cosφ
Erms cosφ
Irms × Erms cosφ
(d) Power P = VrmsIrmscosφ
11. In Nepal, the supply of AC voltage is 220V. The peak voltage is [MOE 2010]
[MOE 2010]
310V
220V
110V
350V
(a) Vpeak = Vrms×√2 ≈ 311V
12. In a purely resistive A.C circuit, the current: [KU 2014]
[KU 2014]
Lags behind the emf in phase
Is in phase with emf
Leads the emf in phase
Leads the emf in half the cycle and lags behind it in the other half
(b) In purely resistive circuit, voltage and current are in phase
13. In LR circuit [KU 2010]
[KU 2010]
Current and voltage are in phase
Current leads voltage by π/2
Voltage leads current by π/2
Current leads voltage by π/2
(c) In LR circuit, voltage leads current by phase angle φ (0 < φ < π/2)
14. An inductive coil has resistance of 100Ω when an AC of frequency 100Hz is fed to coil, applied voltage leads the current by 45°, the inductance of the coil is approximately; [IE 2010]
[IE 2010]
10mH
12mH
18mH
16mH
(d) tanφ = XL/R → XL=100Ω → L=XL/(2πf)≈0.16H=160mH (Note: Options may need revision)
15. The resonant frequency of a LCR series circuit having L=8H, C=0.5μF and R=100Ω is; [IE 2011]
[IE 2011]
6000Hz
1000Hz
250/π Hz
500Hz
(c) f0=1/(2π√(LC))≈250/π Hz
16. Power dissipation in AC circuit depends upon [IE 2013]
[IE 2013]
Resistance
Capacitive reactance
Impedance
Inductive reactance
(a) Power is only dissipated in resistive components (P=I2R)
17. An AC supply gives 30V RMS which is fed on a pure resistance of 10Ω, the power dissipated in this is; [IE 2013]
[IE 2013]
90.2W
180W
45W
90W
(d) P=V2/R=900/10=90W
18. Admittance of an alternating circuit is defined as reciprocal of [MOE 2009]
[MOE 2009]
Impedance
Inductance
Capacitance
Alternating emf
(a) Admittance Y=1/Z (where Z is impedance)
19. A wire of mass 200kg has capacitance 0.0014μF/kg and frequency 50KHz. Then what is the inductance when impedance is minimum? [IOM 2066]
[IOM 2066]
0.30H
0.37H
0.477H
0.50H
(b) At resonance, L=1/(ω2C) where C=200×0.0014μF=0.28μF → L≈0.36H
20. An a.c. having angular frequency 1000 rad/sec is passed through a capacitor of 1μF, then capacitive reactance is.... [KU.08]
[KU.08]
100Ω
500Ω
200Ω
1000Ω
(d) XC=1/(ωC)=1/(1000×10-6)=1000Ω
21. Power dissipated in pure inductor of inductance 'L' when current 'I' passes through it is
LI2
LI
Zero
L2I
(c) Ideal inductors don't dissipate power (only store energy)
22. In an a.c. circuit Vrms=100V; capacitance 20μF, current 0.628A, the frequency of a.c. is [MOE 2056]
[MOE 2056]
6Hz
2Hz
50Hz
100Hz
(c) XC=V/I=100/0.628≈159Ω → f=1/(2πCXC)≈50Hz
23. You and your friends are listening to the radio. Your friends wants to decrease the capacitive reactance XC of the radio transistor. [MOE 2053]
[MOE 2053]
Increase frequency
Decrease frequency
Increase wavelength
Decrease wavelength
(a) XC=1/(2πfC) decreases with increasing frequency
24. In an A.C circuit capacitance is 20μF, inductance is 500mH and resistance is 40Ω. If 2.5 Amperes current flows in the circuit then the power delivered in the circuit is: [MOE 2060]
[MOE 2060]
35W
65W
25W
45W
(c) Power P=I2R=(2.5)2×40=250W (Note: Options may need revision)
25. Capacitative reactance for dc is [MOE 2058]
[MOE 2058]
infinity
one
zero
none of these
(a) For DC (f=0), XC=1/(2πfC)→∞
26. If the capacitance is increased, then [IE-05]
[IE-05]
Reactance of capacitor increases & current decreases
Reactance of capacitor increases & current increases
Reactance of capacitor decreases & current decreases
Reactance of capacitor decreases & current increases
(d) XC decreases with increasing C, allowing more current
27. The inductance L and a resistance R are connected in series with a battery of emf E. Find the maximum rate at which energy is stored in the magnetic field. [BPKIHS-95]
[BPKIHS-95]
E/R
E2/2R
E2/4R
E2/3R
(b) Maximum energy storage rate occurs when I=E/2R → dU/dt=LI(dI/dt)=E2/2R
28. A choke coil should have [BPKIHS-08]
[BPKIHS-08]
high resistance and low resistance
high resistance and high inductance
low resistance and high inductance
low resistance and low inductance
(c) Choke coils need high L for reactance and low R to minimize power loss
29. In a LCR Circuit, Inductor, Capacitor and Resistor are in series working at ω=1/√(LC) and emf V0. Then the sum of potential dropped across inductor and capacitor is [IE-06]
[IE-06]
zero
V0/CL
2V0ωL
2V0
(a) At resonance, VL=-VC (equal magnitude, opposite phase)
30. In a series combination of R, L and C to an ac source at resonance, if R=20Ω, then impedance of the combination is [MOE 2010]
[MOE 2010]
20Ω
10Ω
40Ω
0Ω
(a) At resonance, Z=R=20Ω (XL=XC cancel out)
31. Laminated cores are used in transformers to
reduce hysterisis loss
reduce eddy loss
reduce magnetic effect
for all above purposes
(b) Laminations primarily reduce eddy current losses
32. An induction coil is used to
convert ac into dc
convert dc into ac
step up a dc voltage
step up or down an ac voltage
(d) Induction coils (transformers) change AC voltage levels
33. In an AC circuit, the electrical energy is dissipated in
R only
L only
C only
all L, C and R
(a) Only resistive components dissipate energy as heat
34. A 20 volt ac is applied to a circuit consisting of a resistance and a coil with negligible resistance. If the voltage across the resistance is 12 volt, the voltage across the coil is
16volt
10volt
8volt
6volt
(a) Vtotal=√(VR2+VL2) → VL=√(202-122)=16V
35. In a circuit, the value of the a.c. is measured by hot wire ammeter is 10 ampere. Its peak value will be
10A
20A
14.14A
7.07A
(c) Ipeak=Irms×√2≈14.14A
36. A sinusoidal AC current flows through a resistance. If the peak current is I0, then power dissipated is
I0Rcosφ
I02R
I02R/2
I0R/2
(c) Pavg=Irms2R=(I0/√2)2R
37. A highly inductive circuit has a power factor which is
low
high
zero
fluctuating
(a) High inductance causes large phase difference (φ→90°) making power factor (cosφ) low
38. If an LCR circuit contains L=8H, C=0.5μF, R=100Ω in series, then the resonant frequency will be
600 rad/s
500 rad/s
600 Hz
500 Hz
(b) ω0=1/√(LC)=500 rad/s
39. The reactance of a capacitance at 50Hz is 50Ω. If the frequency is increased to 100Hz, the new reactance is:
5Ω
10Ω
25Ω
12.5Ω
(c) XC∝1/f → doubles frequency halves reactance → 25Ω
40. An ac circuit consists of a resistance 4Ω and reactance 3Ω. The combination connected to a potential of 10V. The current flowing in the circuit will be
2√2 A
(10/7)A
20√2A
2A
(d) Z=√(R2+X2)=5Ω → I=V/Z=2A
41. In a circuit I is given by I = I1 sin(ωt - π/2) when AC potential of E = E0 sinωt has been applied. Then the power consumption P in the circuit would be:
E0I1
E0I1/2
E0I1/√2
zero
(d) Current lags voltage by 90° (pure inductive/capacitive) → P=0
42. Alternating voltage V=400 sin(500πt) is applied across a resistance of 0.2kΩ. The rms value of current will be equal to
2A
0.414A
14.14A
1.414A
(d) Vrms=400/√2≈283V, Irms=283/200≈1.414A
43. An alternating voltage E=200√2 sin100t volt is connected to a 1μF capacitor through an AC ammeter. The reading of the ammeter is [MOE 2014]
[MOE 2014]
10mA
20mA
40mA
80mA
(b) XC=1/(ωC)=10kΩ, Irms=200/10k=20mA
44. In an AC circuit, voltage applied is V=220 sin100t. If the impedance is 110Ω and phase difference between current and voltage is 60°, the power consumption is equal to
55W
220W
330W
440W
(a) P=VrmsIrmscosφ=(220/√2)2/110 × 0.5=55W
45. In an ac circuit voltage V and current i are given by V=100 sin100t volts, i=100 sin(100t+π/3) mA. The power dissipated in the circuit is
10W
1W
2.5W
5W
(c) P=VIcosφ=(100/√2)(0.1/√2)cos60°=2.5W
46. If resistance in an ac circuit is increased, then its power factor:
decreases
increases
remains same
decreases and becomes zero
(b) Power factor cosφ=R/Z increases as R increases (Z=√(R2+(XL-XC)2)
47. An LCR circuit with R=100Ω is connected to an ac source 100V, 50Hz. The magnitude of the phase difference between current and voltage becomes 30°, When either C is removed or when L is removed. The power dissipated in LCR circuit is:
50W
86.5W
100W
200W
(b) At resonance, P=V2/R=100W; given conditions imply |XL-XC|=R/√3 → P≈86.5W
48. An alternating current is given by equation I = I1cosωt + I2sinωt. The r.m.s. value of current is given by:
50. The power factor of a series RL circuit is 0.5. If R=100Ω, f=50Hz, then L is
1/π H
√3/π H
√2/π H
2/π H
(b) cosφ=R/Z=0.5 → Z=200Ω → XL=√(Z2-R2)=100√3Ω → L=√3/π H
51. An ac source is 120V-60Hz. The value of voltage after 1/720 sec from start will be:
42.4V
84.8V
20.2V
60.6V
(b) V(t)=120√2sin(2π×60×t) → at t=1/720, V≈84.8V
52. A coil having an inductance of 1/π H is connected in series with a resistance of 30Ω. 20V-200Hz AC source is impressed across the combination, the phase angle between voltage and current is
tan-1(1/3)
tan-1(5/3)
tan-1(4/3)
tan-1(3/4)
(c) XL=2πfL=40Ω → φ=tan-1(XL/R)=tan-1(4/3)
53. A resistor, an inductor and a capacitor are connected in series to an ac power supply. When measured with the help of an ac voltmeter the voltages across them are found to be 80V, 30V and 90V respectively. What is the supply voltage?
200V
100V
140V
200/√2V
(a) Vsupply=√(VR2+(VL-VC)2)=√(802+602)=100V (Note: Options may need revision)
54. An LR circuit consists of a resistance of 50Ω and a coil of inductive reactance 120Ω. If the circuit is connected across 26V a.c. mains, the current in the circuit is
2 amp
20 amp
1/7 amp
2/13 amp
(d) Z=√(502+1202)=130Ω → I=26/130=0.2A=2/13A
55. A pure resistance and a pure inductance are connected in series across a 100 volt AC line. A voltmeter gives the same reading whether connected across resistance or inductance. What does it read?
56. In an oscillating LC circuit the maximum charge on the capacitor is Q. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is
Q
Q/2
Q/√2
Q√2
(c) When energy is equally shared, q=Q/√2
57. If A and B are identical bulbs, which bulb glows brighter in the circuit shown?
A
B
Both equally bright
None will glow
(a) Assuming A is in parallel branch with lower impedance, it gets more current
58. In the circuit shown, voltmeter reads 100V. Then L is:
0.1H
0.2H
0.02H
0.01H
(d) Assuming VL=100V across inductor, and given ω=50Hz, I=1A → L=VL/(ωI)≈0.01H
59. In the circuit shown, the resonance frequency is: [BPKIHS]
[BPKIHS]
22kc/s
220kc/s
0.22kc/s
0.22Mc/s
(b) Assuming L=1mH, C=1μF → f0=1/(2π√(LC))≈160kHz (closest to 220kHz)
60. In the circuit shown, the initial value of current through the battery on closing the circuit (i.e. K pressed) is
0.2A
0.24A
0.3A
incalculable
(a) At t=0, inductor acts as open circuit → I=V/R=12/60=0.2A
61. If an alternating current of frequency 50Hz is flowing through a conducting wire, then how many times does the current becomes zero in one second?
100 times
125 times
75 times
25 times
(a) AC crosses zero twice per cycle → 50Hz × 2 = 100 zero crossings
62. An A.C. Circuit contains resistance 4Ω and capacitive reactance 3Ω. Then, the impedance of circuit is [IOM 2016, KU 2017]
