What is the value of inductance L for which the current is maximum in a series LCR circuit with C = 10$\mu$F and $\omega$ = 1000 ${\mathrm{s}}^{-1}$?

1.  1 mH

2.  cannot be calculated unless R is known

3.  10 mH

4.  100 mH

The primary and secondary coils of a transformer have 5O and 1500 turns respectively. If the magnetic flux $\varphi$ linked with the primary coils is given by $\varphi$ = ${\varphi }_0$ + 4t, where $\varphi$ is in webers, t is time in second and ${\varphi }_0$ is a constant, the output voltage across the secondary coil is

1.  120 V

2.  220 V

3.  30 V

4.  90 V

The power dissipated in an LCR series circuit connected to an A.C. source of emf $\epsilon$ is

1.  $\frac{{\epsilon }^2\sqrt{R^2 + {\left(L\omega - {\displaystyle \frac{1}{C\omega }}\right)}^2}}{R}$

2.  $\frac{{\epsilon }^2\left[R^2 + {\left(L\omega - \frac{1}{C\omega }\right)}^2\right]}{R}$

3.  $\frac{{\epsilon }^{2}R}{\sqrt{R^2 + {\left(L\omega - \frac{1}{C\omega }\right)}^2}}$

4.  $\frac{{\epsilon }^{2}R}{\left[R^2 + {\left(L\omega - \frac{1}{C\omega }\right)}^2\right]}$

In the given circuit the reading of voltmeter $V_1$ and $V_2$ are 300V each. The reading of the voltmeter ${\mathrm{V}}_3$ and ammeter A are respectively

1.  100 V, 2.0 A

2.  150 V, 2.2 A

3.  220 V, 2.2 A

4.  220 V, 2.0 A

A 220 V input is supplied to a transformer. The output circuit draws a current of 2.0 A at 440 V. If the efficiency of the transformer is 80%, the current drawn by the primary windings of the transformer is

1.  5.0 A

2.  3.6 A

3.  2.8 A

4.  2.5 A

An ac voltage is applied to a resistance R and inductor L in series. If R and the inductive reactance are both equal to 3 $\Omega$, the phase difference between the applied voltage and the current in the circuit is

1.  zero

2.  $\pi$/6

3.  $\pi$/4

4.  $\pi$/2

In an ac circuit an alternating voltage e = $200\sqrt{2}$ sin100t V is connected to capacitor of capacity 1 $\mu F$. rms value of the current in the circuit is

1.  20 mA

2.  10 mA

3.  100 mA

4.  200 mA

A coil has resistance 30$\Omega$ and inductive reactance 20$\Omega$ at 50 Hz frequency. If an ac source, of 200V, 100 Hz, is connected across the coil, the current in the coil will be

1.  2.0 A

2.  4.0 A

3.  8.0 A

4.  $\frac{20}{\sqrt{13}}$ A

In an electrical circuit R, L, C, and an AC voltage source are all connected in series. When L is removed from the circuit, the phase difference between the voltage and the current in the circuit is $\mathrm{\pi }$/3. If C is removed from the circuit, the phase difference is again $\mathrm{\pi }$/3. The power factor of the circuit is

1.  $\frac{1}{2}$

2.  $\frac{1}{\sqrt{2}}$

3.  1

4.  $\frac{\sqrt{3}}{2}$

A small-signal voltage $V\left(t\right) = V_0 \sin \omega t$ is applied across an ideal capacitor C

1.  Current I(t) is in phase with voltage V(t)

2.  current I(t) leads voltage V(t) by 180$°$

3.  current I(t) lags voltage V(t) by 90$°$

4.  Over a full cycle, the capacitor C does not consume any energy from the voltage source.