WBCHSE Class 12 Physics Alternating Current Multiple Questions And Answers

Class 12 Physics Electromagnetic Induction And Alternating Current

Alternating Current Multiple Questions And Answers

Question 1. The internal resistance and internal reactance of an alternating current generator are R_g and X_g respectively. Power from this source is supplied to a load consisting of resisting Rg and reactance X_L. For maximum power to be delivered from the generator to the load. The value of X_L is equal to

1. Zero
2. X_g
3. -X_g
4. R_g

Answer: 3. -X_g

For maximum power, total reactance is zero.

Question 2. To reduce the resonant frequency in an LCR series circuit with a generator,

1. The frequency of the generator should be reduced
2. Another capacitor should be connected in parallel with the first capacitor
3. The iron core of the inductor should be removed
4. The dielectric in the capacitor should be removed

Answer: 2. Another capacitor should be connected in parallel with the first capacitor

∴ \(f=\frac{1}{2 \pi \sqrt{L C}}\)

To reduce f either L or C or both has to be increased.

Question 3. Which of the following combinations should be selected for fine-tuning an LCR circuit used for communication?

1. R = 20 Ω, L = 1.5 H, C= 35 μF
2. R = 25 Ω, L = 2.5 H, C = 45 μF
3. R = 15 Ω, L = 3.5 H, C= 30 μR
4. R = 25 Ω, L = 1.5 H, C = 45 μF

Answer: 3. R = 15 Ω, L = 3.5 H, C= 30 μR

LCR circuit used for communication should have a high Q-factor, \(Q=\frac{1}{R} \sqrt{\frac{L}{C}}\).

Question 4. The current through an ac circuit first increases and then decreases as its frequency is increased. Which among the following are most likely combination of the circuit?

1. Inductorand capacitor
2. Resistorandinductor
3. Resistor and capacitor
4. Resistor, inductor, and capacitor

Answer:

2. Resistorandinductor

4. Resistor, inductor and capacitor

Question 5. The current through an ac (series) circuit increases as the source frequency is increased. Which of the following is the most suitable combination of the circuit?

1. Only resistor
2. A resistor and an inductor
3. A resistor and a capacitor
4. Only capacitor

Answer:

3. Resistor and a capacitor

4. Only capacitor

WBBSE Class 12 Alternating Current MCQs

Question 6. When an ac voltage of 220 V is applied to a capacitor C

1. The maximum voltage between plates is 220 V
2. The current is in phase with the applied voltage
3. The charge on the plates is in phase with the applied voltage
4. The power delivered to the capacitor is zero

Answer:

3. The charge on the plates is in phase with the applied voltage

4. Power delivered to the capacitor is zero

P = v_rms I_rms cos Φ

∴ P = 0 [∴ Φ = 900 ]

Question 7. The line that draws the power supply to your house has

1. Zero average current
2. 220 V average voltage
3. Voltage and current out of phase by 90°
4. Voltage and current possibly differ in phase Φ such that \(|\phi|<\frac{\pi}{2}\)

Answer:

1. Zero average current

4. Voltage and current possibly differing in phase <p such that \(|\phi|<\frac{\pi}{2}\)

Since the line draws ac, the average current is zero. Again, since the line has some resistance (R ≠ 0), there is some phase difference between the voltage and current.

Question 8. An alternating current is given by the equation \(I=i_1 \sin \omega t+i_2 \cos \omega t\). The rms current is given by

1. \(\left(i_2+i_1\right) / \sqrt{2}\)
2. \(\left(i_2-i_1\right) / \sqrt{2}\)
3. \(\sqrt{\left\{\left(i_1^2+i_2^2\right) / 2\right\}}\)
4. \(\sqrt{\left\{\left(i_1^2+i_2^2\right) /(\sqrt{2})\right\}}\)

Answer: 3. \(\sqrt{\left\{\left(i_1^2+i_2^2\right) / 2\right\}}\)

Question 9. An ac having a peak value of 1.41 A is used to heat a wire. A dc producing the same heating rate will be of

1. 1.41 A
2. 2.0 A
3. 0.705 A
4. 1.0 A

Answer: 4. 1.0 A

Question 10. The general equation for the instantaneous voltage of a 50 Hz generator with a peak voltage of 220 V is

1. 220 sin 50 πt
2. 220 sin l00 πf
3. ± 220 sin l00 πt
4. 220 sin 25 π t

Answer: 2. 220 sin l00 πf

Question 11. The relation between angular velocity (ω) and driving frequency (f) of an alternating current is

1. ω = 27 πf
2. \(\omega=\frac{2 \pi}{f}\)
3. \(f=\frac{2 \pi}{\omega}\)
4. f =27 πω

Answer: 1. ω = 27 πf

Question 12. The form factor of an alternating voltage is the ratio of

1. Peak value and rms value
2. Peak value and average value
3. rms value and average value
4. rms value and peak value

Answer: 3. rms value and average value

Question 13. The value of an ac voltage at time 0 < t < \(\frac{\pi}{\omega}\) is given by V= V0 Sinot and at time \(\frac{\pi}{\omega} < t < \frac{2 \pi}{\omega}\) is given by V = -V0 Sin cyf. The average value of V for a complete cycle is

1. \(\frac{V_0}{\sqrt{2}}\)
2. \(\left(\frac{2}{\pi}\right) \mathrm{v}_0\)
3. \(\frac{V_0}{2}\)
4. Zero

Answer: 2. \(\left(\frac{2}{\pi}\right) \mathrm{v}_0\)

Question 14. The rms value of the potential difference V is shown.

1. \(\frac{V_0}{\sqrt{3}}\)
2. \(V_0\)
3. \(\frac{V_0}{\sqrt{2}}\)
4. \(\frac{V_0}{2}\)

Answer: 3. \(\frac{V_0}{\sqrt{2}}\)

Hint: In this case, V = V₀, when 0 ≤ t ≤ \(\frac{T}{2}\)

= 0, when \(\frac{T}{2}\) ≤ t ≤ T

∴ \(V_{\mathrm{rms}}^2=\frac{\int_0^T V^2 d t}{\int_0^T d t}=\frac{1}{T} V_0^2\left[\int_0^{T / 2} d t\right]=\frac{V_0^2}{2}\)

or, \(V_{\mathrm{rms}}=\frac{V_0}{\sqrt{2}}\)

Short Answer Questions on Alternating Current

Question 15. The rms value and frequency of an AC are 5A and 50 Hz respectively. The value of the current after \(\frac{1}{300}\)s from the time when its value becomes zero is

1. \(5 \sqrt{2} \mathrm{~A}\)
2. \(5 \sqrt{\frac{3}{2}} \mathrm{~A}\)
3. \(\frac{5}{6} \mathrm{~A}\)
4. \(\frac{5}{\sqrt{2}} \mathrm{~A}\)

Answer: 2. \(5 \sqrt{\frac{3}{2}} \mathrm{~A}\)

Hint: \(I=I_0 \sin \omega t=5 \sqrt{2} \sin \left(100 \pi \times \frac{1}{300}\right)\)

= \(5 \sqrt{2} \times \frac{\sqrt{3}}{2}=5 \sqrt{\frac{3}{2}} \mathrm{~A}\)

Series AC Circuits with R, L, C

Question 16. In an AC circuit containing capacitance, only the current

1. Leads the voltage by 180°
2. Is in phase with the voltage
3. Leads the voltage by 90°
4. Lags behind the voltage by 90°

Answer: 3. Leads the voltage by 90°

Question 17. In an LR circuit, the phase angle between alternating voltage and alternating current is 45°. The value of inductive reactance will be

1. \(\frac{R}{4}\)
2. \(\frac{R}{2}\)
3. R
4. Data insufficient

Answer: 3. R

Question 18. In an LCR series circuit, the capacitance is reduced to one-fourth, when in resonance. What change should be made in the inductance, so that the circuit remains in resonance?

1. 4 times
2. \(\frac{1}{4} \text { times }\)
3. 8 times
4. 2 times

Answer: 1. 4 times

Question 19. The phase difference between V and 1 of an LCR circuit in series resonance is

1. π
2. \(\frac{\pi}{2}\)
3. \(\frac{\pi}{4}\)
4. 0

Answer: 4. 0

Question 20. The reactance of an inductor of inductance \(\frac{1}{\pi}\) at frequency 50 Hz is

1. \(\frac{50}{\pi} \Omega\)
2. \(\frac{\pi}{50} \Omega\)
3. 100
4. 50

Answer: 3. 100

Question 21. which quantity in an AC circuit is not dependent on frequency?

1. Resistance
2. Impedance
3. Inductive reactance
4. Capacitative reactance

Answer: 1. Resistance

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Question 22. The condition of getting maximum current in an LCR series circuit is

1. \(X_L=0\)
2. \(X_C=0\)
3. \(X_L=X_C\)
4. \(R=X_L-X_C\)

Answer: 3. \(X_L=X_C\)

Real-Life Applications of AC Power Systems

Question 23. The series resonant frequency of an LCR circuit is f. If the capacitance is made,4, times the initial value, then the resonant frequency will become

1. f/2
2. 2f
3. f
4. f/4

Answer: 1. f/2

Question 24. A coil has a resistance of 30 Ω and inductive reactance of 20 Ω at 50 Hz frequency. If an AC source of 200V, 100 Hz is connected across the coil, the current in the coil will be

1. 2.0 A
2. 4.0 A
3. 8.0 A
4. \(\frac{20}{\sqrt{13}} \mathrm{~A}\)

Answer: 2. 4.0 A

Hint: In this case, R = 30Ω and X_L = 20 Ω

∴ X_L = ωL = 2nfL \f- frequency]

∴ \(\frac{X_L}{X_L^{\prime}}=\frac{f}{f^{\prime}} \quad \text { or, } \quad X_L^{\prime}=X_L \times\left(\frac{f^{\prime}}{f}\right)=20 \times\left(\frac{100}{50}\right)=40 \Omega\)

∴ \(Z=\sqrt{R^2+X_L^{\prime 2}}=\sqrt{(30)^2+(40)^2}=50\)

∴ [laex]I=\frac{V}{Z}=\frac{200}{50}=4 \mathrm{~A}[/latex]

Question 25. A fully charged capacitor C with initial charge q₀ is connected to a coil of self-inductance L at t = 0. The time at which the energy is stored equally between the electric and the magnetic field is

1. \(\frac{\pi}{4} \sqrt{L C}\)
2. \(2 \pi \sqrt{L C}\)
3. \(\sqrt{L C}\)
4. \(\pi \sqrt{L C}\)

Answer: 1. \(\frac{\pi}{4} \sqrt{L C}\)

Hint: During discharging of capacitor C through inductance L, let at any instant, charge in capacitor be Q.

∴ Q = Q₀ sin ωt

Maximum energy storedin capacitor \(=\frac{1}{2} \frac{Q_0^2}{C}\)

Let at an instant t, the energy be stored equally between electric and magnetic field. The energy stored in the electric field instant t is

⇒ \(\frac{1}{2} \frac{Q^2}{C}=\frac{1}{2}\left[\frac{1}{2} \frac{Q_0^2}{C}\right] \quad \text { or, } Q^2=\frac{Q_0^2}{2}\)

or, \(Q=\frac{Q_0}{\sqrt{2}} \quad \text { or, } Q_0 \sin \omega t=\frac{Q_0}{\sqrt{2}}\)

or, \(\omega t=\frac{\pi}{4} \quad \text { or, } t=\frac{\pi}{4 \omega}=\frac{\pi \sqrt{L C}}{4}\)  [∵\(\omega = \frac{1}{\sqrt{L C}}\)

Question 26. A voltage V₀ sincot is applied across a series combination of resistance R and inductor L. The peak value of the current in the circuit is

1. \(\frac{V_0}{\sqrt{R^2+\omega^2 L^2}}\)
2. \(\frac{V_0}{\sqrt{R^2-\omega^2 L^2}}\)
3. \(\frac{V_0}{\sqrt{R^2+\omega^2 L^2}} \sin \omega t\)
4. \(\frac{V_0}{R}\)

Answer: 1. \(\frac{V_0}{\sqrt{R^2+\omega^2 L^2}}\)

Question 27. When an ideal choke is connected to an AC source of 100 V and 50 Hz, a current of 8 A flows through the circuit A current of 10A flows through the circuit when pure resistors are connected instead of the choke coil. If the two are connected in series with an AC supply of 100V and 40 Hz, then the current in the circuit is

1. 10 A
2. 8 A
3. \(5 \sqrt{2} \mathrm{~A}\)
4. \(10 \sqrt{2} \mathrm{~A}\)

Answer: 3. \(5 \sqrt{2} \mathrm{~A}\)

⇒ \(X_L=\omega L=\frac{100}{8}\)

∴ \(L=\frac{100}{8 \omega}=\frac{1}{8 \pi} \text { and } R=\frac{100}{10}=10 \Omega\)

When R and L are connected in series,

∴ \(Z=\sqrt{\left(\frac{1}{8 \pi} \times 2 \pi \times 40\right)^2+10^2}=10 \sqrt{2}\)

∴ \(I=\frac{V}{Z}=\frac{100}{10 \sqrt{2}}=5 \sqrt{2} \mathrm{~A}\)

Question 28. In an LCR circuit voltages across R, L, and C are 10V, 10V, and 20V respectively. The voltage between the two endpoints of the whole combination is

1. 30 V
2. 10√3 V
3. 20 V
4. 10√2 V

Answer: 4. 10√2 V

Question 29. In an ac circuit alternating voltage E = 200√2 sin100t volt is connected to a capacitor of capacity 1μF. The rms value of the current in the circuit is

1. 10 mA
2. 100 mA
3. 200 mA
4. 20 mA

Answer: 4. 20 mA

Hint: From the given equation, we may write

E₀ = 200√2 V and ω = 100 rad/s

∴ \(X_C=\frac{1}{\omega C}=\frac{1}{100\left(1 \times 10^{-6}\right)}=10^4 \Omega\)

∴ \(I_{\mathrm{rms}}=\frac{E_{\mathrm{rms}}}{X_C}=\frac{\frac{E_0}{\sqrt{2}}}{X_C}=\frac{\frac{200 \sqrt{2}}{\sqrt{2}}}{10^4}=20 \mathrm{~mA}\)

Practice Problems on Alternating Current

Question 30. In the given network, readings of the ammeter (A) and the voltmeter (V) are respectively

1. 800 V, 2 A
2. 220 V, 2.2 A
3. 300 V, 2 A
4. 100 V, 2 A

Answer: 2. 800 V, 2 A

Power in AC Circuits

Question 31. The power factor of an LR circuit carrying an ac of angular frequency ω is

1. \(\frac{R}{\omega L}\)
2. \(\frac{\omega L}{R}\)
3. \(\frac{R}{\sqrt{R^2+\omega^2 L^2}}\)
4. \(\frac{R}{\sqrt{R^2-\omega^2 L^2}}\)

Answer: 3. \(\frac{R}{\sqrt{R^2+\omega^2 L^2}}\)

Question 32. One of the conditions for getting a wattless current in an ac circuit is

1. I = 0
2. C = 0
3. R = 0
4. L = C

Answer: 3. R = 0

Question 33. If an emf E = E₀ cos ωt is applied to a circuit, the current becomes I = I₀ cos ωt What is the power factor of the circuit?

1. Zero
2. \(\frac{1}{\sqrt{2}}\)
3. 1
4. ∞

Answer: 3. 1

Question 34. In an ac circuit, V and I are given by V = 100sin(100 t) V, and I = \(100 \sin \left(100 t+\frac{\pi}{3}\right)\) A respectively. The power dissipated in the circuit is

1. 10⁴ W
2. 10 W
3. 2500 W
4. 5 W

Answer: 3. 2500 W

Hint: From the given equations for V we get,

v₀  = 100 v, I₀ and θ = \(\frac{\pi}{3}\)

Power, P = \(\frac{V_0 I_0}{2} \cos \theta=\frac{100 \times 100}{2} \cos \frac{\pi}{3}=2500 \mathrm{~W}\)

LC Oscillations

Question 35. The inductance and capacitance in a closed circuit are 20 mH and 2μF respectively. The natural frequency will be

1. 796 Hz
2. 5000 Hz
3. 40 Hz
4. 31400 Hz

Answer: 1. 796 Hz

Question 36. For an LC oscillator which one of the following is not true?

1. It converts DC to AC current
2. It can be used as a filter
3. It can sustain stable oscillations only for frequencies less than the resonance frequency
4. The resonance frequency is radians per second

Answer: 3. It can sustain stable oscillations only for frequencies less than the resonance frequency

AC Generator and Transformer

Question 37. An ideal transformer is used to decrease an alternating voltage from 880 V to 220 V. If the number of turns of its primary coil is 4000, then what is that in the secondary coil?

1. 16000
2. 4000
3. 2000
4. 1000

Answer: 4. 1000

Common Questions on AC Theory and Applications

Question 38. The core of any transformer is laminated to

1. Increase the secondary voltage
2. Reduce the energy loss due to eddy currents
3. Reduce the energy loss due to hysteresis
4. Make it robust

Answer: 2. Reduce the energy loss due to eddy currents

Question 39. In a non-ideal transformer, the primary and secondary voltages and currents are V₁, I_1, and V₂, I₂ respectively. The efficiency of the transformer is

1. \(\frac{V_2}{V_1}\)
2. \(\frac{I_2}{I_1}\)
3. \(\frac{V_2 I_2}{V_1 I_1}\)
4. \(\frac{V_1 I_1}{V_2 I_2}\)

Answer: 3. \(\frac{V_2 I_2}{V_1 I_1}\)

Question 40. The turns ratio of an ideal transformer is 1: n. The input-to-output power transfer ratio is

1. 1:1
2. l:n
3. n:1
4. 1: n²

Answer: 1. 1:1

Question 41. For the circuit,

1. Mean value = I₀
2. rms value = \(\frac{I_0}{\sqrt{2}}\)
3. Form factor = 1
4. Form factor = \(\frac{1}{\sqrt{2}}\)

Answer:

1. Mean value = I₀

3. Form factor = 1

Question 42. An emf of V = V₀sin ωt is applied on a series LCR circuit. If there is no phase difference between the voltage and current, then

1. \(I=\frac{V_0}{R} \sin \omega t\)
2. \(\omega L=\frac{1}{\omega C}\)
3. Effective power = \(\frac{V_0^2}{R}\)
4. Ratio of terminal potential difference across L and R = \(\frac{1}{\omega C R}\)

Answer:

1. \(I=\frac{V_0}{R} \sin \omega t\)

2. \(\omega L=\frac{1}{\omega C}\)

4. ratio of terminal potential difference across L and R = \(\frac{1}{\omega C R}\)

Question 43. A coil of resistance 8 Ω and self-inductance 19.1 mH is connected with an AC source of peak voltage 200 V and frequency 50 Hz

1. Reactance due to induction = 0.955 Ω
2. The impedance of the circuit = 10 Ω
3. rms value of current = 10√2 Ω
4. Power dissipated = 2000 W

Answer:

2. The impedance of the circuit = 10 Ω

3. RMS value of current = 10√2 Ω

4. Power dissipated = 2000 W

Question 44. If only a capacitor is connected to an AC circuit

1. Wattless current is obtained
2. The current is 90° ahead of the voltage
3. The current lags the voltage by 90°
4. Effective power is inversely proportional to cuC

Answer:

1. Wattless current is obtained

2. The current is 90° ahead of voltage

Examples of AC Circuit Calculations

Question 45. The alternating current in an alternating circuit is given by I – I₀ sin ωt. In this case

1. The time taken by the current to reach maximum value I0 from zero is \(\frac{\pi}{2 \omega}\)
2. The time taken by the current to reach maximum value I0 from zero is \(\frac{\pi}{4 \omega}\)
3. The time taken by the current to reach rms value from zero is \(\frac{\pi}{4 \omega}\)
4. The time taken by the current to reach -I0 from zero is \(\frac{\pi}{\omega}\)

Answer:

1. The time taken by the current to reach maximum value I0 from zero is \(\frac{\pi}{2 \omega}\)

3. The time taken by the current to reach rms value from zero is \(\frac{\pi}{4 \omega}\)

Question 46. In a series LCR circuit the resonant frequency f₀, alternating voltage V = V₀ sin ωt and current I = I₀ sin(ωt+ θ). So if frequency

1. f < f₀ then θ > 0
2. f < f₀ then θ < 0
3. f > f₀ then θ > 0
4. f > f₀ then θ <0

Answer:

1. f < f₀ then θ > 0

4. f > f₀ then θ <0

Question 47. In an ideal transformer, the number of turns in the primary and secondary is N₁ and N₂, and current and power in the input and output are I₁, I₂, and P₁, P₂ respectively. Then

1. \(I_2=I_1 \frac{N_1}{N_2}\)
2. \(I_2=I_1 \cdot \frac{N_2}{N_1}\)
3. P₂ = P₁
4. \(P_2=P_1 \cdot \frac{N_1}{N_2}\)

Answer:

1. \(I_2=I_1 \frac{N_1}{N_2}\)

3. P₂ = P₁

Question 48. L, C, and R represent the inductance, capacitance, and reactance respectively. Which of the following combinations have the same dimensions as that of frequency?

1. \(\frac{1}{R C}\)
2. \(\frac{R}{L}\)
3. \(\frac{1}{\sqrt{L C}}\)
4. \(\frac{C}{L}\)

Answer:

1. \(\frac{1}{R C}\)
2. \(\frac{R}{L}\)
3. \(\frac{1}{\sqrt{L C}}\)

Question 49. In a resonant LCR circuit,

1. The power factor is zero
2. The power factor is one
3. Dissipated in the resistor is zero
4. The power dissipated in the capacitor is zero

Answer:

2. The Power factor is one

4. The Power dissipated in the capacitor is zero

Question 50. Two LR circuits are shown. The change in current in this circuit is shown. Choose the correct options.

1. R₁ > R₂
2. R₁ = R₂
3. L₁ > L₂
4. L₁ < L₂

Answer:

2. R₁ = R₂

4. L₁ < L₂