Q1. What is the r.m.s. value of an alternating current which when passed through a resistor produces heat which is thrice of that produced by a direct current of 2 amperes in the same resistor :-

1. 6 amp
2. 2 amp
3. 3.46 amp
4. 0.66 amp

Correct Answer: C. 3.46 amp

Q2. The peak value of an alternating e.m.f. which is given by \(E=E_{0} \cos \omega t\) is 10 volts and its frequency is 50 Hz. At time \(t=\frac{1}{600}\text{ s}\), the instantaneous e.m.f. is

1. 10 V
2. \(5\sqrt{3}\text{ V}\)
3. 5 V
4. 1 V

Correct Answer: B. \(5\sqrt{3}\text{ V}\)

Q3. The phase difference between current and voltage in an AC circuit is \(\frac{\pi}{4}\) radian. If the frequency of AC is 50 Hz, then the phase difference is equivalent to the time difference:-

1. 0.78 s
2. 15.7 ms
3. 2.5 s
4. 2.5 ms

Correct Answer: D. 2.5 ms

Q4. A current in circuit is given by \(i=3+4 \sin \omega t\). Then the effective value of current is :

1. 5
2. \(\sqrt{7}\)
3. \(\sqrt{17}\)
4. \(\sqrt{10}\)

Correct Answer: C. \(\sqrt{17}\)

Q5. Incorrect statements are:
(a) A.C. meters can measure D.C also
(b) If A.C. meter measures D.C. their scale must be linear and uniform
(c) A.C. and D.C. meters are based on heating effect of current
(d) A.C. meter reads rms value of current

1. a, b
2. b, c
3. c, d
4. d, a

Correct Answer: B. b, c

Q6. The r.m.s. value of current for a variable current \(i=i_{1} \cos \omega t + i_{2} \sin \omega t\) :-

1. \(\frac{1}{\sqrt{2}}(i_{1}+i_{2})\)
2. \(\frac{1}{\sqrt{2}}(i_{1}+i_{2})^{2}\)
3. \(\frac{1}{\sqrt{2}}(i_{1}^{2}+i_{2}^{2})^{1/2}\)
4. \(\frac{1}{2}(i_{1}^{2}+i_{2}^{2})^{1/2}\)

Correct Answer: C. \(\frac{1}{\sqrt{2}}(i_{1}^{2}+i_{2}^{2})^{1/2}\)

Q7. The relation between an A.C. voltage source and time in SI units is :
\(V=120 \sin (100 \pi t) \cos (100 \pi t)\) volt. Value of peak voltage and frequency will be respectively :-

1. 120 volt and 100 Hz
2. \(\frac{120}{\sqrt{2}}\) volt and 100 Hz
3. 60 volt and 200 Hz
4. 60 volt and 100 Hz

Correct Answer: D. 60 volt and 100 Hz

Q8. If an A.C. main supply is given to be 220 V. What would be the average e.m.f. during a positive half cycle :-

1. 198 V
2. 386 V
3. 256 V
4. None of these

Correct Answer: A. 198 V

Q9. The hot wire ammeter measures :-

1. D.C. current
2. A.C. current
3. None of above
4. both (1) & (2)

Correct Answer: D. both (1) & (2)

Q10. Frequency of A.C. in India is

1. 45 Hz
2. 60 Hz
3. 50 Hz
4. None of the above

Correct Answer: C. 50 Hz

Q11. For an alternating current \(I=I_{0} \cos \omega t\), What is the rms value and peak value of current :-

1. \(\frac{I_{0}}{\sqrt{2}}\), \(\frac{I_{0}}{2}\)
2. \(\frac{I_{0}}{\sqrt{2}}\), \(I_{0}\)
3. \(I_{0}\), \(\frac{I_{0}}{\sqrt{2}}\)
4. \(2I_{0}\), \(\frac{I_{0}}{\sqrt{2}}\)

Correct Answer: B. \(\frac{I_{0}}{\sqrt{2}}\), \(I_{0}\)

Q12. If a step up transformer have turn ratio 5, frequency 50 Hz root mean square value of potential difference on primary 100 volts and the resistance of the secondary winding is 500 \(\Omega\) then the peak value of voltage in secondary winding will be (the efficiency of the transformer is hundred percent)

1. \(500\sqrt{2}\)
2. \(10\sqrt{2}\)
3. \(50\sqrt{2}\)
4. \(20\sqrt{2}\)

Correct Answer: A. \(500\sqrt{2}\)

Q13. A resonant A.C. circuit contains a capacitor of capacitance \(10^{-6}\text{ F}\) and an inductor of \(10^{-4}\text{ H}\). The frequency of electrical oscillations will be :-

1. \(10^{5}\text{ Hz}\)
2. \(10\text{ Hz}\)
3. \(\frac{10^{5}}{2\pi}\text{ Hz}\)
4. \(\frac{10}{2\pi}\text{ Hz}\)

Correct Answer: C. \(\frac{10^{5}}{2\pi}\text{ Hz}\)

Q14. A resistance of 300 \(\Omega\) and an inductance of \(\frac{1}{\pi}\) henry are connected in series to a A.C. voltage of 20 volts and 200 Hz frequency. The phase angle between the voltage and current is :-

1. \(\tan^{-1}(\frac{4}{3})\)
2. \(\tan^{-1}(\frac{3}{4})\)
3. \(\tan^{-1}(\frac{3}{2})\)
4. \(\tan^{-1}(\frac{2}{3})\)

Correct Answer: A. \(\tan^{-1}(\frac{4}{3})\)

Q15. The graphs depict the dependence of two reactive impedances \(X_{1}\) and \(X_{2}\) on the frequency of the alternating e.m.f. applied individually to them. If the curve for \(X_1\) is a hyperbola and \(X_2\) is a linear line starting from origin, we can say that :

1. \(X_{1}\) is an inductor and \(X_{2}\) is a capacitor
2. \(X_{1}\) is a resistor and \(X_{2}\) is a capacitor
3. \(X_{1}\) is a capacitor and \(X_{2}\) is an inductor
4. \(X_{1}\) is an inductor and \(X_{2}\) is a resistor

Correct Answer: C. \(X_{1}\) is a capacitor and \(X_{2}\) is an inductor

Q16. A 12 ohm resistor and a 0.21 henry inductor are connected in series to an AC source operating at 20 volts, 50 cycle/second. The phase angle between the current and the source voltage is:

1. \(30^{\circ}\)
2. \(40^{\circ}\)
3. \(80^{\circ}\)
4. \(90^{\circ}\)

Correct Answer: C. \(80^{\circ}\)

Q17. A 110 V, 60 W lamp is run from a 220 V AC mains using a capacitor in series with the lamp, instead of a resistor then the voltage across the capacitor is about:-

1. 110 V
2. 190 V
3. 220 V
4. 311 V

Correct Answer: B. 190 V

Q18. The resistance that must be connected in series with inductance of 0.2 H in order that the phase difference between current and e.m.f. may be \(45^{\circ}\) when the frequency is 50 Hz, is:-

1. 6.28 ohm.
2. 62.8 ohm.
3. 628 ohm.
4. 31.4 ohm.

Correct Answer: B. 62.8 ohm.

Q19. A student connects a long air cored coil of manganin wire to a 100 V D.C. supply and records a current of 25 amp. When the same coil is connected across 100 V, 50 Hz a.c. the current reduces to 20 A, the reactance of the coil is :-

1. 4 \(\Omega\)
2. 3 \(\Omega\)
3. 5 \(\Omega\)
4. None

Correct Answer: B. 3 \(\Omega\)

Q20. The graph shows variation of I with f for a series R-L-C network. Keeping L and C constant. If R decreases :
(a) Maximum current \((I_{m})\) increases
(b) Sharpness of the graph increases
(c) Quality factor increases
(d) Band width increases

1. a, b, c
2. b, c, d
3. c, d, a
4. All

Correct Answer: A. a, b, c

Q21. Alternating current is flowing in inductance L and resistance R. The frequency of source is \(\omega/2\pi\). Which of the following statement is correct:

1. For low frequency the limiting value of impedance is L.
2. For high frequency the limiting value of impedance is \(\omega L\).
3. For high frequency the limiting value of impedance is R.
4. For low frequency the limiting value of impedance is \(\omega L\).

Correct Answer: B. For high frequency the limiting value of impedance is \(\omega L\).

Q22. 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

1. Bulb will give more intense light.
2. Bulb will give less intense light.
3. Bulb will give light of same intensity as before
4. Bulb will stop radiating light.

Correct Answer: A. Bulb will give more intense light.

Q23. In an A.C. circuit resistance and inductance are connected in series. The potential and current in inductance is:

1. \(V_{0}\) sin \(\omega t\), \(\frac{V_{0}}{\omega L}\) sin \(\omega t\)
2. \(V_{0}\) sin \(\omega t\), \(\frac{V_{0}}{\omega L} \sin(\omega t+\pi/2)\)
3. \(V_{0} \sin(\omega t+\pi/2)\), \(\frac{V_{0}}{\omega L}\) sin \(\omega t\)
4. \(V_{0}\) sin (\(\omega t\) + \(\pi/2\)), \(\frac{V_{0}}{\omega L}\sin(\omega t-\pi/2)\)

Correct Answer: C. \(V_{0} \sin(\omega t+\pi/2)\), \(\frac{V_{0}}{\omega L}\) sin \(\omega t\)

Q24. An a.c. source of voltage V and of frequency 50 Hz is connected to an inductor of 2 H and negligible resistance. A current of r.m.s value I flows in the coil. When the frequency of the voltage is changed to 400 Hz keeping the magnitude of V the same, the current is now :-

1. 8 I in phase with V
2. 4 I and leading by \(90^{\circ}\) from V
3. \(\frac{I}{4}\) and lagging by \(90^{\circ}\) from V
4. \(\frac{I}{8}\) and lagging by \(90^{\circ}\) from V

Correct Answer: D. \(\frac{I}{8}\) and lagging by \(90^{\circ}\) from V

Q25. A capacitor of capacity C is connected in A.C. circuit. The applied emf is \(V=V_{0} \sin \omega t\), then the current is:

1. \(I = \frac{V_{0}}{\omega L} \sin \omega t\)
2. \(I=\frac{V_{0}}{\omega L}\sin(\omega t+\pi/2)\)
3. \(I=V_{0}\) C \(\sin \omega t\)
4. \(I=V_{0}\omega C \sin(\omega t+\pi/2)\)

Correct Answer: D. \(I=V_{0}\omega C \sin(\omega t+\pi/2)\)

Q26. The impedance of a circuit, when a resistance R and an inductor of inductance L are connected in series in an A.C. circuit of frequency (f) is :-

1. \(\sqrt{R+4\pi fL^{2}}\)
2. \(\sqrt{R+4\pi^{2}f^{2}L^{2}}\)
3. \(\sqrt{R^{2}+4\pi^{2}f^{2}L^{2}}\)
4. \(\sqrt{R^{2}+2\pi^{2}f^{2}L^{2}}\)

Correct Answer: C. \(\sqrt{R^{2}+4\pi^{2}f^{2}L^{2}}\)

Q27. A capacitor of capacity C and reactance X if capacitance and frequency become double then reactance will be :-

1. 4X
2. \(\frac{X}{2}\)
3. \(\frac{X}{4}\)
4. 2X

Correct Answer: C. \(\frac{X}{4}\)

Q28. The coil of choke in a circuit :

1. increases the current
2. controlled the current
3. has high resistance to d.c. circuit
4. does not change the current

Correct Answer: B. controlled the current

Q29. The inductive reactance of an inductive coil with \(\frac{1}{\pi}\) henry and 50 Hz :-

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

Correct Answer: C. 100 ohm

Q30. In the L-R circuit \(R=10\Omega\) and \(L=2\text{H}\). If 120 V, 60 Hz alternating voltage is applied then the flowing current in this circuit will be :-

1. 0.32 A
2. 0.16 A
3. 0.48 A
4. 0.80 A

Correct Answer: B. 0.16 A

Q31. An inductance of 0.4 Henry and a resistance of 100 ohm are connected to a A.C. voltage source of 220 V and 50 Hz. Then find out the phase difference between the voltage and current flowing in the circuit :

1. \(\tan^{-1}(2.25 \pi)\)
2. \(\tan^{-1}(0.4 \pi)\)
3. \(\tan^{-1}(1.5 \pi)\)
4. \(\tan^{-1}(0.5 \pi)\)

Correct Answer: B. \(\tan^{-1}(0.4 \pi)\)

Q32. A capacitor of capacitance 100 \(\mu\)F & a resistance of 100 \(\Omega\) is connected in series with AC supply of 220V, 50Hz. The current leads the voltage by :

1. \(\tan^{-1}(\frac{1}{2\pi})\)
2. \(\tan^{-1}(\frac{1}{\pi})\)
3. \(\tan^{-1}(\frac{2}{\pi})\)
4. \(\tan^{-1}(\frac{4}{\pi})\)

Correct Answer: B. \(\tan^{-1}(\frac{1}{\pi})\)

Q33. If the current through an inductor of inductance L is given by \(I=I_{0}\) sin \(\omega t\), then the voltage across inductor will be :

1. \(I_{0}\) L sin (\(\omega t\) – \(\pi/2\))
2. \(I_{0} \omega L \sin(\omega t + \pi/2)\)
3. \(I_{0}\) sin (\(\omega t\) – \(\pi\))
4. None of these

Correct Answer: B. \(I_{0} \omega L \sin(\omega t + \pi/2)\)

Q34. There is a 5 \(\Omega\) resistance in an A.C., circuit. Inductance of 0.1 H is connected with it in series. If equation of A.C. e.m.f. is 5 sin 50 t then the phase difference between current and e.m.f. is :-

1. \(\frac{\pi}{2}\)
2. \(\frac{\pi}{6}\)
3. \(\frac{\pi}{4}\)
4. 0

Correct Answer: C. \(\frac{\pi}{4}\)

Q35. A 50 Hz a.c. source of 20 volts is connected across R and C as shown in figure. The voltage across R is 12 volts. The voltage across C is :

1. 8 V
2. 16V
3. 10 V
4. Not possible to determine unless values of R and C are given

Correct Answer: B. 16V