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1.

The capacity of a pure capacitor is 1 farad. In dc circuits, its effective resistance will be 
1. Zero
2. Infinite
3. 1 ohm
4. 1/2 ohm

2.

When an alternating voltage is given as; \(E = (6 \sin\omega t - 2 \cos \omega t)~\text V,\) what is its RMS value?
1. \(4 \sqrt 2 ~\text V\) 
2. \(2 \sqrt 5 ~\text V\) 
3. \(2 \sqrt 3 ~\text V\) 
4. \(4 ~\text V\) 

3. What is the instantaneous power of a resistor having resistance \(R\) across an AC supply of \(E= E_0\sin(\omega t)\)?

1.	\(\dfrac{E_{0}^{2}}{R} \sin^{2}\omega t\)	2.	\(\dfrac{E_{0}^{2}}{R}\cos^{2}\omega t\)
3.	\(\dfrac{E_{0}^{2}}{R}\)	4.	\(\text{zero}\)

4. In the network shown below what is the reading of the AC voltmeter?
     

1.	Zero	2.	\(100\) V
3.	\(200\) V	4.	\(500\) V

5.

A: When the frequency of the AC source in a series LCR circuit equals to the resonant frequency, the reactance of the circuit is zero.
R: There is maximum current through the inductor as well as a capacitor at resonance.
1. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
2. If both Assertion & Reasons are true but the reason is not the correct explanation of the assertion, then mark (2)
3. If Assertion is a true statement but the reason is false, the mark (3)
4. If both Assertion and Reason are false statements, then mark (4)
 

6.

The circuit is in a steady state when the key is at position \(1\). If the switch is changed from position \(1\) to position \(2\), then the steady current in the circuit will be:

1.	\(E_o \over R\)	2.	\(E_o \over 3R\)
3.	\(E_o \over 2R\)	4.	\(E_o \over 4R\)

7. A bulb is rated at \(100\) V, \(100\) W, and is treated as a resistor. The inductance of an inductor (choke coil) that should be connected in series with the bulb to operate the bulb at its rated power with the help of an AC source of \(200\) V and \(50\) Hz is:
1. \(\dfrac{\pi }{\sqrt{3}}~\text{H}\)
2. \(100~\text{H}\)
3. \(\dfrac{\sqrt{2}}{\pi }~\text{H}\)
4. \(\dfrac{\sqrt{3}}{\pi }~\text{H}\)

8. It is found that the current through the \(LCR\) series circuit is at its maximum. If \(V_r, V_C~\text{and}~V_L\) are potential differences across resistance, capacitor, and inductor respectively, then which of the following is correct?

1.	\(V_r=V_L>V_C\)
2.	\(V_R \neq V_L=V_C\)
3.	\(V_R \neq V_L \neq V_C\)
4.	\(V_R=V_C \neq V_L\)

9.

In a box \(Z\) of unknown elements (\(L\) or \(R\) or any other combination), an ac voltage \(E = E_0 \sin(\omega t + \phi)\) $$is applied and the current in the circuit is found to be \(I = I_0 \sin\left(\omega t + \phi +\frac{\pi}{4}\right)\). The unknown elements in the box could be:
             

1.	Only the capacitor
2.	Inductor and resistor both
3.	Either capacitor, resistor, and an inductor or only capacitor and resistor
4.	Only the resistor

10.

A coil of inductive reactance 31 $\Omega$ has a resistance of 8$\Omega$. It is placed in series with a condenser of capacitative reactance 25$\Omega$. The combination is connected to an a.c. source of 110 volt. The power factor of the circuit is
(1) 0.80
(2) 0.33
(3) 0.56
(4) 0.64

11.

A capacitor of capacitance \(1~\mu\text{F}\) is charged to a potential of \(1\) V. It is connected in parallel to an inductor of inductance \(10^{-3}~\text{H}\). What is the value of the maximum current that will flow in the circuit?
1. \(\sqrt{1000}~\text{mA}\)
2. \(1~\text{mA}\)
3. \(1~\mu\text{F}\)
4. \(1000~\text{mA}\)

12.

A transistor-oscillator using a resonant circuit with an inductance \(L\) (of negligible resistance) and a capacitance \(C\) has a frequency \(f.\) If \(L\) is doubled and \(C\) is changed to \(4C,\) the frequency will be:
1. \(f/4\)
2. \(8f\)
3. \(f/2\sqrt2\)
4. \(f/2\)

13.

A loss-free transformer having 100 turns in primary is used to transmit 10 kW of power. The input voltage is 200 V and power is transmitted at 5 kV. The currents in the primary and secondary coils of the transformer are-
(1) 2 A and 50 A
(2) 50 A and 2 A
(3) 25 A and 4 A
(4) 12.5 A and 8 A

14.

The core of a transformer is laminated so that:

1.	energy losses due to eddy currents may be minimized
2.	the weight of the transformer may be reduced
3.	rusting of the core may be prevented
4.	the ratio of voltage in primary and secondary may be increased