CBSE Class 12 Physics Alternating Current Important Questions Worksheet Set B

1 What is an alternating voltage? Give an equation to represent the same. 

2 Explain how a resistor responds to an alternating voltage with relevant equations. Give the graphical representations of current and voltage across the resistor. 

3 Define mean value of current and derive the relation between the peak value of current and mean value of current. What is the value of average power consumed in a complete cycle? 

4 Define the rms value of current. Derive the relation between the peak value and rms value of current. 

5 A light bulb is rated at 100 W for a 220 V supply. Find (a) the resistance of the bulb ;

(b) the peak voltage of the source; and (c) the rms current through the bulb. 

6 What is a phasor? Give the phasor diagram showing the voltage and current phasors and their relationship at time t in case of an ac source connected to a resistor.

7 Explain how an inductor responds to an alternating voltage with relevant equations. Give the phasor diagram for the same. 

8 Show that the average power through an ac circuit consisting of inductor over one complete cycle is zero. 

9 A pure inductor of 25 mH is connected to a source of 220 V. Find the inductive reactance and rms current in the circuit if the frequency of the source is 50 Hz.

10 Give the formula to find the reactance due to an inductor. What is the function of reactance in a circuit? What is the relationship between the current and voltage when alternating current is allowed to flow through an ac circuit? Explain 

11 Explain what happens to ac current when it is allowed to flow through a circuit consisting of a capacitor. What is the phase relationship between the current and voltage? 

Important Questions for NCERT Class 12 Physics Alternating Current

Question. If we decrease the frequency of the applied A.C. with a purely capacitive load, do (1) the amplitude of Vc and (2) amplitude of Ic increase, decrease of remain the same. 
(a) (1) increase (2) same
(b) (1) same (2) increase
(c) (1) same (2) decrease
(d) (1) decrease (2) same

Answer: C

Question. An inductor coil of inductance L is cut into two equal parts and both the parts are connected in parallel. The net inductance is : 
(a) L
(b) L/2
(c) L/4
(d) 2 L.

Answer: C

Question. An inductance L having a resistance R is connected to an alternating source of angular frequency w. The Quality factor Q of inductance is 
(a) R/ wL
(b) (wL/R)2
(c) (R /wL)1/2
(d) wL/R

Answer: D

Question. In an A.C. circuit, the current flowing in inductance is I = 5 sin (100 t – p/2) amperes and the potential difference is V = 200 sin (100 t) volts. The power consumption is equal to 
(a) 1000 watt
(b) 40 watt
(c) 20 watt
(d) zero

Answer: D

Question. L, C, R represent physical quantities inductance, capacitance and resistance respectively. The combinations which have the dimensions of frequency are 
(a) 1/RC
(b) R/L
(c) 1/ LC
(d) C/L

Answer: C

Question. An inductance L having a resistance R is connected to an alternating source of angular frequency w. The Quality factor Q of inductance is 
(a) R/ wL
(b) (wL/R)2
(c) (R /wL)½
(d) wL/R

Answer: D

Question. A step down transformer is connected to 2400 volts line and 80 amperes of current is found to flow in output load. The ratio of the turns in primary and secondary coil is 20 : 1. If transformer efficiency is 100%, then the current flowing in the primary coil will be 
(a) 1600 amp
(b) 20 amp
(c) 4 amp
(d) 1.5 amp

Answer: C

Question. The mutual inductance of a pair of coils, each of N turns, is M henry. If a current of I ampere in one of the coils is brought to zero in t second, the emf induced per turn in the other coil, in volt, will be
(a) MI /t
(b) NMI /t
(c) MN /It
(d) MI /Nt

Answer: A

Question. An A.C. circuit containing only capacitance, the current : 
(a) lags the voltage by 90°
(b) leads the voltage by 90°
(c) remains in phase with voltage
(d) leads the voltage in 180°

Answer: B

Question. A choke coil has: 
(a) Low inductance and low resistance
(b) High inductance and high resistance
(c) Low inductance and high resistance
(d) High inductance and low resistance

Answer: D

Question. The tuning circuit of a radio receiver has a resistance of 50W, an inductor of 10 mH and a variable capacitor. A 1 MHz radio wave produces a potential difference of 0.1 mV. The values of the capacitor to produce resonance is (Take Π² = 10) 
(a) 2.5 pF
(b) 5.0 pF
(c) 25 pF
(d) 50 pF

Answer: A

Question. A coil has resistance 30 ohm and inductive reactance 20 ohm at 50 Hz frequency. If an ac source, of 200 volt, 100 Hz, is connected across the coil, the current in the coil will be 
(a) 4.0 A
(b) 8.0 A
(c) 20√13 A
(d) 2.0 A

Answer: A

Question. The primary winding of a transformer has 500 turns whereas its secondary has 5000 turns. The primary is connected to an A.C. supply of 20 V, 50 Hz. The secondary will have an output of
(a) 2 V, 50 Hz
(b) 2 V, 5 Hz
(c) 200 V, 50 Hz
(d) 200 V, 500 Hz.

Answer: C

Question. A coil of 40 henry inductance is connected in series with a resistance of 8 ohm and the combination is joined to the terminals of a 2 volt battery. The time constant of the circuit is
(a) 5 seconds
(b) 1/5 seconds
(c) 40 seconds
(d) 20 seconds

Answer: A

Question. An ideal coil of 10H is connected in series with a resistance of 5W and a battery of 5V. After 2 sec the connection is made, the current flowing in ampere in the circuit is 
(a) (1 – e–1)
(b) (1 – e)
(c) e
(d) e–1

Answer: A

Question. An inductor, a resistor and a capacitor are joined in series with an AC source. As the frequency of the source is slightly increased from a very low value, the reactance of the
(a) inductor increases
(b) resistor increases
(c) capacitor increases
(d) circuit increases

Answer: C

Question. In an A.C. circuit, Irms and I0 are related as
(a) Irms = ΠI0
(b) Irms = √2 I0
(c) Irms = I0/Π
(d) Irms = I0 /√ 2

Answer: C

Question. Two cables of copper are of equal lengths. One of them has a single wire of area of cross-section A, while other has 10 wires of cross-sectional area A/10 each. Give their suitability for transporting A.C. and D.C.
(a) only multiple strands for A.C., either for D.C.
(b) only multiple strands for A.C., only single strand for D.C.
(c) only single strand for D.C., either for A.C.
(d) only single strand for A.C., either for D.C.

Answer: A

Question. A coil of self-inductance L is connected in series with a bulb B and an AC source. Brightness of the bulb decreases when
(a) a capacitance of reactance XC = XL is included in the same circuit.
(b) an iron rod is inserted in the coil.
(c) frequency of the AC source is decreased.
(d) number of turns in the coil is reduced.

Answer: B

Question. In an ac circuit an alternating voltage 200 2 sin100 t volts is connected to a capacitor of capacity 1 mF. The r.m.s. value of the current in the circuit is
(a) 10 mA
(b) 100 mA
(c) 200 mA
(d) 20 mA 

Answer: D

Question. An LCR series circuit, connected to a source E, is at resonance. Then the voltage across
(a) R is zero
(b) R equals applied voltage
(c) C is zero
(d) L equals applied voltage

Answer: B

Question. Energy in a current carrying coil is stored in the form of
(a) electric field
(b) magnetic field
(c) dielectric strength
(d) heat

Answer: B

Question. In a RLC circuit capacitance is changed from C to 2 C. For the resonant frequency to remain unchanged, the inductance should be changed from L to
(a) 4 L
(b) 2 L
(c) L/2
(d) L/4

Answer: C

Question. The tuning circuit of a radio receiver has a resistance of 50 W , an inductor of 10 mH and a variable capacitor. A 1 MHz radio wave produces a potential difference of 0.1 mV. The values of the capacitor to produce resonance is (Take π² = 10)
(a) 2.5 pF
(b) 5.0 pF
(c) 25 pF
(d) 50 pF

Answer: A

Question. A.C. power is transmitted from a power house at a high voltage as
(a) the rate of transmission is faster at high voltages
(b) it is more economical due to less power loss
(c) power cannot be transmitted at low voltages
(d) a precaution against theft of transmission lines

Answer: B

Question. In a circuit L, C and R are connected in series with an alternating voltage source of frequency f. The current leads the voltage by 45°. The value of C is
(a) 1/πf (2πfL - R)
(b) 1/2πf (2πfL - R)
(c) 1/πf (2πfL + R)
(d) 1/2πf (2πfL + R)

Answer: D

Question. In an A.C. circuit, the current flowing in inductance is I = 5 sin (100 t – π/2) amperes and the potential difference is V = 200 sin (100 t) volts. The power consumption is equal to
(a) 1000 watt
(b) 40 watt
(c) 20 watt
(d) Zero

Answer: D

Question. In the given circuit the reading of voltmeter V₁ and V₂ are 300 volt each. The reading of the voltmeter V₃ and ammeter A are respectively 

(a) 150 V and 2.2 A
(b) 220 V and 2.2 A
(c) 220 V and 2.0 A
(d) 100 V and 2.0 A

Answer: B

Question. An inductance of negligible resistance whose reactance is 22 Ω at 200 Hz is connected to 200 volts, 50 Hz power line. The value of inductance is
(a) 0.0175 henry
(b) 0.175 henry
(c) 1.75 henry
(d) 17.5 henry

Answer: A

Question. The power factor of an AC circuit having resistance (R) and inductance (L) connected in series and an angular velocity w is
(a) R/ωL
(b) R/(R² + ω²L²)^1/2
(c) ωL/R
(d) R/(R² – ω²L²)^1/2

Answer: B

Question. An inductive coil has a resistance of 100 W. When an a.c. signal of requency 1000 Hz is fed to the coil, the applied voltage leads the current by 45°. What is the inductance of the coil ?
(a) 10 mH
(b) 12 mH
(c) 16 mH
(d) 20mH.

Answer: C

Question. An AC voltage source has an output of V = 200sin 2πft .
This source is connected to a 100 Ω resistor. RMS current in the resistance is
(a) 1.41 A
(b) 2.41 A
(c) 3.41 A
(d) 0.71 A

Answer: A

Question. In the circuit shown in fig, the resonant frequency is 

(a) 75 kc/s
(b) 750 kc/s
(c) 7.5 kc/s
(d) 75 mc/s

Answer: A

Question. A 12 Ω resistor and a 0.21 henry inductor are connected in series to an a.c. source operating at 20 volt, 50 cycle. The phase angle between the current and source voltage is
(a) 30º
(b) 40º
(c) 80º
(d) 90º

Answer: C

Question. If resistance of 100Ω, and inductance of 0.5 henry and capacitance of 10 × 10⁶ farad are connected in series through 50 Hz A.C. supply, then impedance is
(a) 1.8765 Ω
(b) 18.76 Ω
(c) 187.6 Ω
(d) 101.3 Ω

Answer: C

Question. An alternating current is given by
i = i₁ cosωt + i₂ sinwt
The rms current is given by 

Answer: C

Question. A capacitor in an ideal LC circuit is fully charged by a DC source, then it is disconnected from DC source, the current in the circuit
(a) becomes zero instantaneously
(b) grows , monotonically
(c) decays monotonically
(d) oscillate infinitely

Answer: A

Question. If the rms current in a 50 Hz AC circuit is 5 A, the value of the current 1/300 s after its value becomes zero is
(a) 5√2A
(b) 5√3/2 A
(c) 5/6 A
(d) 5/√2A

Answer: B

Question. A bulb and a capacitor are connected in series to a source of alternating current. If its frequency is increased, while keeping the voltage of the source constant, then bulb will
(a) give more intense light
(b) give less intense light
(c) give light of same intensity before
(d) stop radiating light

Answer: A

Question. Determine the rms value of the emf given by E (in volt) = 8 sin (ω t) + 6sin (2ωt)
(a) 5 √2V
(b) 7 √2V
(c) 10 V
(d) 10 √2V

Answer: A

MATCH THE FOLLOWING 

Write the dimensional formula of the following 8 marks

1 Rms value of current -----------------------

2 rms voltage-------------------------------

3 Capacitive reactance-------------------------------

4 Inductive reactance-----------------------------

5 Power factor-------------------------------------------

6 Q-factor-------------------------------------------------

7 Resonant frequency----------------------------------

8 Impedance of LCR series circuit------------------------

Important Questions for NCERT Class 12 Physics Alternating Current

Question. A transformer having efficiency of 90% is working on 200 V and 3 kW power supply. If the current in the secondary coil is 6 A, the voltage across the
secondary coil and the current in the primary coil respectively are
(a) 300 V, 15 A
(b) 450 V, 15 A
(c) 450 V, 13.5 A
(d) 600 V, 15 A

Answer B

Question. The primary of a transformer when connected to a dc battery of 10 volt draws a current of 1 mA. The number of turns of the primary and secondary windings are 50 and 100 respectively. The voltage in the secondary and the current drawn by the circuit in the secondary are respectively
(a) 20 V and 2.0 mA
(b) 10 V and 0.5 mA
(c) Zero volt and therefore no current
(d) 20 V and 0.5 mA 

Answer C

Question. A capacitor of capacity C has reactance X. If capacitance and frequency become double then reactance will be
(a) 4X
(b) X/2
(c) X/4
(d) 2X

Answer C

Question. A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is p/3.
If instead C is removed from the circuit, the phase difference is again p/3 between current and voltage.
The power factor of the circuit is
(a) zero
(b) 0.5
(c) 1.0
(d) –1.0 

Answer C

Question. A coil has resistance 30 ohm and inductive reactance 20 ohm at 50 Hz frequency. If an ac source, of 200 volt, 100 Hz, is connected across the coil, the current in the coil will be
(a) 2.0 A
(b) 4.0 A
(c) 8.0 A
(d) 20 /√13a

Answer B

Question. What is the value of inductance L for which the current is maximum in a series LCR circuit with C = 10 mF and w = 1000 s–1?
(a) 1 mH
(b) cannot be calculated unless R is known
(c) 10 mH
(d) 100 mH

Answer D

Question. An series L-C-R circuit is connected to a source of A.C. current. At resonance, the phase difference between the applied voltage and the current in the circuit, is
(a) Π
(b) zero
(c) Π/4
(d) Π/2

Answer B

Question. An inductor 20 mH, a capacitor 100 mF and a resistor 50 W are connected in series across a source of emf, V = 10 sin 314t. The power loss in the circuit is
(a) 0.79 W
(b) 0.43 W
(c) 2.74 W
(d) 1.13 W

Answer A

Question. The potential differences across the resistance, capacitance and inductance are 80 V, 40 V and 100 V respectively in an L-C-R circuit. The power factor of this circuit is
(a) 0.4
(b) 0.5
(c) 0.8
(d) 1.0

Answer C

Question. An inductor 20 mH, a capacitor 50 mF and a resistor 40 W are connected in series across a source of emf V = 10 sin 340t. The power loss in A.C. circuit is
(a) 0.76 W
(b) 0.89 W
(c) 0.51 W
(d) 0.67 W

Answer C

Question. In an electrical circuit R, L, C and ac voltage source are all connected in series. When L is removed fromthe circuit, the phase difference between the voltage and the current in the circuit is p/3. If instead, C is removed from the circuit, the phase difference is again Π/3. The power factor of the circuit is
(a) 1/2
(b) 1/√2
(c) 1
(d) 3/√2

Answer C

Question. A coil of inductive reactance 31 W has a resistance of 8 W. It is placed in series with a condenser of capacitative reactance 25 W. The combination is connected to an a.c. source of 110 V. The power factor of the circuit is
(a) 0.33
(b) 0.56
(c) 0.64
(d) 0.80

Answer D

Question. In an a.c. circuit with phase voltage V and current I, the power dissipated is
(a) V.I
(b) depends on phase angle between V and I
(c) 1 /2 ×V.I
(d) 1/√2×V.I 

Answer B

Question. In an A.C. circuit, the current flowing is I = 5 sin (100t – Π/2) ampere and the potential difference is V = 200 sin (100t) volts. The power consumption is equal to
(a) 20 W
(b) 0 W
(c) 1000 W
(d) 40 W

Answer B

Question. A transistor-oscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produces oscillations of frequency f. If L is doubled and C is changed to 4C, the frequency will be
(a) f/2
(b) f/4
(c) 8f
(d) f /2√2

Answer D

Question. A 220 volt input is supplied to a transformer. The output circuit draws a current of 2.0 ampere at 440 volts. If the efficiency of the transformer is 80%, the current drawn by the primary windings of the transformer is
(a) 3.6 ampere
(b) 2.8 ampere
(c) 2.5 ampere
(d) 5.0 ampere 

Answer D

Question. The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux f linked with the primary coil is given by f = f0 + 4t, where f is in webers, t is time in seconds and f0 is a constant, the output voltage across the secondary coil is
(a) 120 volts
(b) 220 volts
(c) 30 volts
(d) 90 volts 

Answer A

Question. A transformer is used to light a 100 W and 110 V lamp from a 220 V mains. If the main current is 0.5 amp, the efficiency of the transformer is approximately
(a) 50%
(b) 90%
(c) 10%
(d) 30% 

Answer B

Question. The core of a transformer is laminated because
(a) ratio of voltage in primary and secondary may be increased
(b) energy losses due to eddy currents may be minimised
(c) the weight of the transformer may be reduced
(d) rusting of the core may be prevented. 

Answer B

Question. A step-up transformer operates on a 230 V line and supplies a load of 2 ampere. The ratio of the primary and secondary windings is 1 : 25. The current in the primary is
(a) 15 A
(b) 50 A
(c) 25 A
(d) 12.5 A 

Answer B

Question. The time constant of C-R circuit is
(a) 1/CR
(b) C/R
(c) CR
(d) R/C

Answer C

Question. A series R-C circuit is connected to an alternating voltage source. Consider two situations :
(i) When capacitor is air filled.
(ii) When capacitor is mica filled.
Current through resistor is i and voltage across capacitor is V then
(a) ia > ib
(b) Va = Vb
(c) Va < Vb
(d) Va > Vb

Answer D

Question. An ac voltage is applied to a resistance R and an inductor L in series. If R and the inductive reactance are both equal to 3 W, the phase difference between the applied voltage and the current in the circuit is
(a) Π/6
(b) Π/4
(c) Π/2
(d) zero 

Answer B