Chapter 7 Alternating Current MCQs

1.

An ideal inductor is connected across an AC source of voltage. The current in the circuit.

(a) is ahead of the voltage in phase by 𝜋. (b) lags voltage in phase by 𝜋.

(c) is ahead of voltage in phase by 𝜋 /2. (d) lags voltage in phase by 𝜋/2.

2.

An inductor, a capacitor and a resistor are connected in series across an ac source of voltage. If the frequency of the source is decreased gradually, the reactance of:

(a) both the inductor and the capacitor decreases.

(b) inductor decreases and the capacitor increases.

(c) both the inductor and the capacitor increases.

(d) inductor increases and the capacitor decreases.

3.

Which of the following statements about a series LCR circuit connected to an ac source is correct?

(a) If the frequency of the source is increased, the impedance of the circuit first decreases and then increases.

(b) If the net reactance (XL – XC) of circuit becomes equal to its resistance, then the current leads the voltage by 45°.

(c) At resonance, the voltage drop across the inductor is more than that across the capacitor.

(d) At resonance, the voltage drop across the capacitor is more than that across the inductor.

4.

The selectivity of a series LCR a.c. circuit is large, when

(a) L is large and R is large  (b) L is small and R is small

(c) L is large and R is small  (d) L = R

5.

The power factor of a series LCR circuit at resonance will be

(a) 1 (b) 0 (c) ½ (d) 1/√2

6.

A voltage signal is described by:

V  = V0 for , V= 0 for for a cycle. Its rms value is

(a) (b) V0 (c) (d)

7.

The figure shows variation of current (I) with time (t) in four devices P, Q, R and S. The device in which an alternating current flows is:

(a) P (b) Q (c) R (d) S

8.

An ac voltage v = v0 sin ωt is applied to a series combination of a resistor R and an element X. The instantaneous current in the circuit is Then which of the following is correct?

(a) X is a capacitor and (b) X is an inductor and XL = R

(c) X is an inductor and (d) X is a capacitor and XC = R

9.

What is the ratio of inductive and capacitive reactance in an ac circuit?

(a) ω2 LC (b) LC2 (c) (d) ω2 L

10.

Two statements are given one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.

Assertion (A) : The mutual inductance between two coils is maximum when the coils are wound on each other.

Reason (R) : The flux linkage between two coils is maximum when they are wound on each other.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

(C) Assertion (A) is true, but Reason (R) is false.

(D) Assertion (A) is false and Reason (R) is also false.

11.

Which of the following quantity/quantities remains same in primary and secondary coils of an ideal transformer?  Current, Voltage, Power, Magnetic flux  

(A) Current only (B) Voltage only

(C) Power only (D) Magnetic flux and Power both  

12.

A resistor and an ideal inductor are connected in series to a , 50 Hz ac source. When a voltmeter is connected across the resistor or the inductor, it shows the same reading. The reading of the voltmeter is :  

(A) (B) 100 V (C) (D) 50 V  

13.

Figure shows the variation of inductive reactance XL of two ideal inductors of inductance L1 and L2, with angular frequency ω. The value of is

(A) (B) (C) 3 (D)

14.

The phase difference between electric field and magnetic field in an electromagnetic wave propagating along z-axis is-

(A) zero (В) π (C) (D)

15.

A bulb is rated 40W for a 220 V supply. The peak voltage of the supply is

(a) (b) 220 V (c) (d) 440 V

16.

An a.c voltage is applied to a resistor of resistance 5 Ω and an inductor having inductive reactance of 5Ω connected in series. The phase difference between applied voltage and the current in the circuit is:

(a) (b) (c) (d) zero

17.

A pure inductor of 70 mH is connected to a source of 220 V. The frequency of the source is 50 Hz. The current in the circuit is

(a) 10.0A (b) 3.15A (c) 4.4A (d) 5A

18.

The value of current through an inductor of inductance 2.0 H and negligible resistance when  connected to an AC source of 157 V, 50 Hz will be:

(a) 78.5A (b) 1.57A (c) (d)

19.

A bulb and an iron core inductor are connected to an AC source through key as shown in figure

The bulb glows with certain brightness. Now iron rod in taken out of the inductor. Then the brightness of bulb.

(a) Increases  (b) Decreases

(c) Is unchanged (d) First increases then decreases

20.

For which of the following, a capacitor acts as an infinite resistance component in the circuit?

(a) Alternating current

(b) Direct current

(c) Alternating current as well as direct current 

(d) Neither alternating current nor direct current

21.

A e. m. f. Es = 50 sin 314t is applied across a pure capacitor of 637 μF. The instantaneous current I is:

(a) 10 cos 314 t A (b) 50 cos 314 t A (c) 20 cos 314 t A (d) 20 sin 314 t A

22.

The instantaneous power supplied to a capacitor is given by

Pc = im cos(ωt)vm sin(ωt)  

The average power over a complete cycle would be

(a)   (b) (c) zero (d) – 1

23.

An ac source of emf V(t) = V0 sinωt is put across a pure capacitor. The value of angular frequency of instantaneous power is:

(a) 0 (b) ω (c) 2ω (d)

24.

A 25 μF capacitor, a 0.10 H inductor and a 25 Ω resistor are connected in series with an ac source of emf E = 310 sin 314 t. What is the frequency of AC source?

(a) 314 Hz (b) 100 Hz (c) 50 Hz (d) 310 Hz

25.

Which of the following combinations should be used for better tuning of an LCR circuit used for communication?

(a) R = 25 Ω, L = 1.5H, C = 35μF (b) R = 25 Ω, L = 2.0H, C = 45μF

(c) R = 15 Ω, L = 3.5H, C = 30μF (d) R = 15 Ω, L = 1.0H, C = 40μF

26.

A series LCR circuit is connected to a 220 V variable frequency (a.c) supply. If L = 20mH, μF and R = 110 Ω. The frequency of the source, for which the average power absorbed by the circuit is maximum will be:

(a) 125 Hz (b) 250 Hz (c) 350 Hz (d) 500 Hz

27.

In the circuit shown ac source gives a Voltage V=20 cos 2000t. Neglecting source resistance, the voltmeter and Ammeter reading will be.

(a) 0 V, 1.4 A (b) 1.68 V, 0.47 A (c) 0 V, 14A (d) 5.6 V, 1.4A

28.

A resistor, an inductor and a capacitor are connected in series with a variable frequency source of alternating emf. At resonance, the amplitude of current depends on:

(A) Resistance (B) Inductance (C) Capacitance (D) Frequency of source

Choose the correct answer from the options given below:

(a) (A) only (b) (A) and (D) only

(c) (A), (B) and (C) only  (d) (D) only

29.

A resistor, a capacitor and an inductor are joined in series with an alternating current source. If the frequency of the source is slightly increased from a very low value, then:

(a) Resistance of resistor decreases. (b) Capacitive reactance increases.

(c) Inductive reactance increases. (d) Impedance increases.

30.

A series L.C.R circuit with R =3Ω, XL = 10 Ω and XC= 6Ω is connected to an a.c. source. The power  factor of the circuit is:

(a) 0      (b) 0.6     (c) 0.75     (d) 1

31.

If 𝜈 is the frequency of ac mains, then the frequency of sonometer wire at resonance is :

(a) 𝜈/2 (b) v (c) 2𝜈 (d) 4𝜈

32.

In a series LCR circuit L = 4 H, C = 100 μF and R = 25 Ω. The circuit is connected to a variable frequency 220 V source.

The source angular frequency (ω) which drives the circuit in resonance is

(a) 0.05 rad s–1 (b) 2 rad s–1 (c) 314 rad s–1 (d) 50 rad s–1

33.

In a series LCR circuit if frequency of the ac source is increased from resonance value f0 to 2f0. Choose the statement depicting correct situation in the circuit.

 (a) Impedance of the circuit would increase

 (b) Potential difference across the resistance would increase

 (c) rms value of the current in the circuit will increase

 (d) Potential difference across the series combination of L & C will become zero

34.

A pure inductor of 0.25 mH, a pure capacitor of 250 μF and a resistor of 350 Ω are connected in series. An ac source of amplitude 210 V is connected across this series combination of L, C and R. The impedance and current amplitude in the circuit at resonance will be : 

(a) Zmin = 703 Ω and Imax = 0.30 A   (b) Zmin = 350 Ω and Imax = 0.60 A 

(c) Zmin = 850 Ω and Imax = 0.25 A  (d) Zmin = 430 Ω and Imax = 0.5 A

35.

An LCR series circuit containing resistance R1, inductance L1 and capacitance C1 gives resonance at the same frequency f as a second similar combination R2, L2 and C2. If the two circuits are connected in series, then the frequency of the combined circuit is.

(a) 2f (b) 4f (c) f (d).

36.

The current and voltage in ac circuit are given by I = 5sin A and V = 200 sin (100t) V. The power dissipated in the circuit is

(a) 20W (b) 40W (c) 0 (d) 1000 V

37.

What is the power factor of an ac circuit having resistance R and Inductance L connected in series? (ω is the angular frequency)

(a) (ω L) R–1  (b) R (ω L) –1 (c) (d)

38.

The power factor of an ac circuit having resistance R and inductance L connected in series is:

(a) (b) (c) (d)

39.

An AC (220 V, 50 Hz) circuit has a resistance of 3 Ω and an impedance of 5 Ω . The power factor of the circuit will be :

(a) 10 (b) 0.6 (c) Zero (d) 4.4

40.

Which quantity is increased in a step down transformer?

(a) Power (b) Current (c) Frequency (d) Voltage

41.

A transformer has an efficiency of 80%. It works at 3 kW and 120 V. If the secondary voltage is 240 V, what will be the secondary current?

(a) 2.5 A (b) 12.5 A (c) 25 A (d) 10 A 

42.

You are given a transformer that has 800 turns on its primary coil and 64 turns on its secondary coil. A voltage of 220 V is applied to the primary coil. What is the output voltage?

(a)  17.6 V (b) 275 V (c) 176 V (d) 2750 V

New Q

key

Explanations

1.

D

Current in circuit lags exactly by a phase of

2.

B

For indicator

XL = 2 π∫L

For capacitor

Hence on decreasing frequency XL decreases and XC increases.

3.

B

If XL-XC = R

Than  tan φ =1

                   φ = 45°

4.

C

Sharper the resonance curve, more selective will be the LCR circuit. Thus the selectivity of LCR circuit is large when L is large and R is small. Selecting directly proportional to quality factor.

5.

A

At resonance Z = R

⇒ Cos φ =1

6.

C

7.

D

Alternating current is one which changes its direction after a regular interval of time.

8.

D

Current lead by an angle of . Hence CKt. Consists of R – C.

XC = R

Hence X is a capacitor with XC = R

9.

C

10.

A

11.

D

Magnetic flux and power both

12.

A

13.

D

XL = 𝜔L [None of these]

Slope

Note answer b and d is same

14.

A

The phase difference is zero between electric field and magnetic field in an em wave

15.

C

16.

B

tanφ = 1

17.

A

18.

D

V = IXL

19.

A

On pulling iron core out, L will decrease.

⇒ Impedance z will decrease.

⇒ Power of bulb will increase

Since when the iron rod is taken out then the inductance decreases as a result overall current flowing through the circuit increases.

20.

B

  [f = 0 for d.c]

XC = ∞

21.

A

I0 = 10

I = I0 cos ω t

= 10 cos 314t A [∵ Phase difference = ]

22.

C

Zero

23.

C

Frequency of power is double that of voltage

∴ if the voltage waveform has a freq. ‘f’ the power waveform will have a freq. 2f. Therefore angular freq. ‘2 ω’.

24.

C

W = 314

2πf = 314

2 × 3.14f = 314

F = 50 Hz.

25.

C

For turning of LCR circuit, high sensitivity is required.

26.

A

Fr = 125 Hz

27.

D

XL = ω L = 2000 × 5 × 10 -3  = 10 Ω

Xc = 1/wC  = 1 / (2000 × 50 × 10-6)  = 10 Ω

XL = Xc . Hence this is a case of resonance

I = V/R = (20/root2)  × 10 =  1.4A , Voltmeter reading = 1.4 × 4 = 5.6 V

XL = ωL = 2000 × 5 ×10-3 = 10 Ω

XL - XC [case of resonance]

V = 1.4 × 4 = 5.6 V

28.

A

Resonance condition

29.

C

X  increases as frequency increases

XL = 2πfL

30.

B

= 0.6

31.

C

Frequency of sonometer becomes doubled.

32.

A

= 50 rad/sec

33.

B

Impedance is minimum at resonance

34.

B

At resonance

Z = R = 350 Ω

35.

C

Frequency remains same

36.

C

P = Erms Irms cosφ

φ = 90° [cos90°=  0]

37.

D

38.

B

39.

B

40.

B

Voltage decreases and hence current increases

41.

D

Is = 10 Amp.

42.

A