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The natural frequency of the circuit shown in the figure is 

(1) $\frac{1}{2\mathrm{\pi }\sqrt{\mathrm{LC}}}$
(2) $\frac{1}{\mathrm{\pi }\sqrt{\mathrm{LC}}}$
(3) $\frac{2}{\mathrm{\pi }\sqrt{\mathrm{LC}}}$
(4) None of these

A series combination of R, L, C is connected to an a.c. source. If the resistance is 3 $\Omega$ and the reactance is 4 $\Omega$, the power factor of the circuit is
(1) 0.4                  (2) 0.6                   (3) 0.8               (4) 1.0

In an LCR circuit, the capacitance is made one-fourth of its value when it is in resonance. Then what  should be the corresponding change in inductance, so that the circuit remains in resonance?
(1) 4 times         (2) 1/4 times         (3) 8 times         (4) 2 times

An alternating current having peak value 14 A is used to heat a metal wire. To produce the same heating effect, a constant i can be used where i is
(1) 14 A                   (2) about 20 A            (3) 7 A              (4) about 10 A

A step –down transformer transforms a supply line voltage of 2200 volt into 220 volt. The primary coil has 5000 turns. The efficiency and power transmitted by the transformer are 90% and 8 kilowatt respectively. Then the number of turns in the secondary is:
1. 5000     
2. 50       
3. 500         
4. 5

A coil has an inductance of 0.7 H and is joined in series with a resistance of 220 $\Omega$. An alternating emf of 220 V at 50 Hz is applied to it. Then the wattless component of the current in the circuit is
(1) 5 amp         (2) 0.5 amp       (3) 0.7 amp        (4) 7 amp

The voltage and current in a series AC circuit are given by V = $V_0$ cos $\omega t and I = I_0 (\cos \omega t+\frac{\mathrm{\pi }}{3}).$  What is the power dissipated in the circuit?
(1) $\frac{V_0{I}_0}{2}$                (2) 0              (3) $\frac{V_0{I}_0}{4}$         (4) $\frac{\sqrt{3}}{2}{V}_0{I}_0$

In the circuit of figure, what will be the reading of the voltmeter?

(1) 300 V           (2) 900 V
(3) 200 V         (4) 400 V

In a circuit shown in figure, what will be the readings of the voltmeter and ammeter if a.c. source of 200 V and 50 Hz is connected

(1) 800 V, 2A                 (2) 300 V, 2 A
(3) 200 V, 2 A                (4) 100 V, 2 A

The root-mean-square value of an alternating current of 50 Hz frequency is 10 A. The time taken by  the alternating current in reaching from zero to maximum value and peak value will be:
(1) 2×10^–2 s and 14.14 A            (2)  1 × 10^–2 s and 7.07 A
(3) 5×10^–3 s and 7.07 A              (4) 5 × 10^–3 s and 14.14 A

A 120 volt AC source is connected across a pure inductor of inductance 0.70 Henry. If the frequency of the source is 60 Hz, the current passing through the inductor is :
(1) 4.55 A                       (2) 0.325 A
(3) 0.455 A                     (4) 3.25 A

In a LCR circuit capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to
(1) 4 L                (2) 2 L
(3) L/2              (4) L/4

An alternating current flows through a circuit consisting of inductance L and resistance R. Periodicity of the supply is $\omega$/2$\mathrm{\pi }$. Which of the following is true?
(1) the limiting value of impedance is L for low frequency
(2) the limiting value of impedance for low frequency is R
(3) limiting value of impedance for high frequency is R
(4) the limiting value of impendence for low frequency is L$\omega$

In a series R-L-C AC circuit, for a particular value of R, L and C, power supplied by the source is P at resonance. If the  value of inductance is halved, then the power from the source again at resonance is P'. Then
(1) P = $\frac{P\text{'}}{2}$
(2) P = 2P'
(3) P = 4P'
(4) P = P'

In a circuit, capacitor (C=4$\mu$F) is connected in series with a resistor (R=2.5 M$\Omega$) with a battery of 12 V having negligible internal resistance. Find the time after which potential difference across capacitor becomes three times of potential difference across resistor (ln2 = 0.693).
(1) 13.86 s          (2) 1.386 s        (3) 6.93 s           (4) 20 s

Match List I (expression for current) with list II (RMS value of current) and select the correct answer.
                    List I                                               List II
A. I = $I_0\sin \omega t \cos \omega t$                                  (i) $I_0$
B. $I=I_0\sin \left(\omega t+\frac{\mathrm{\pi }}{3}\right)$                                  (ii) $I_0/\sqrt{2}$               
C. $I=I_0\left(\sin \omega t+\cos \omega t\right)$                             (iii) $I_{0}e$
D. $I=I_0\left(e\right)$                                                (iv) $I_0/\left(2\sqrt{2}\right)$
 
               A          B           C          D
(1)          4            2           1          3
(2)          4            2           3           1
(3)          2            4           3            1
(4)          2            4           1            3

In the figure, which voltmeter reads zero, when $\omega$ is equal to the resonant frequency of series LCR circuit?

(1) V₁                 (2) V₂
(3) V₃               (4) None of these

An AC source producing emf $\epsilon ={\epsilon }_0$[cos (100$\pi$s^-1)t + cos (500$\pi$s^–1)t] is connected in series with a capacitor and a resistor. The steady-state current in the circuit is found to be i = i₁cos [(100$\pi$s^-1)t+$\varphi$₁] + i₂cos [(500$\pi$s^-1)t-$\varphi$₂], Then
(1) i₁ > i₂
(2) i₁ = i₂
(3) i₁ < i₂
(4) the information is insufficient to find the relation between i₁ and i₂.

In the a.c. circuit shown in figure, the supply voltage has a constant r.m.s. value $\epsilon$ but variable frequency f. Resonance frequency in Hertz is

(1) 10            (2) 100      (3) 1000         (4) 200