For a series LCR circuit, the power loss at resonance is

1.  $\frac{V^2}{\left(\omega L - {\displaystyle \frac{1}{\omega C}}\right)}$

2.  $I^{2}L\omega$

3.  ${\mathrm{I}}^2\mathrm{R}$

4.  $\frac{V^2}{C\omega }$

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

1.  $\frac{1}{2\mathrm{\pi f}\left(2\mathrm{\pi f} \mathrm{L} - \mathrm{R}\right)}$

2.  $\frac{1}{2\mathrm{\pi f}\left(2\mathrm{\pi f} \mathrm{L} + \mathrm{R}\right)}$

3.  $\frac{1}{\mathrm{\pi f}\left(2\mathrm{\pi f} L - R\right)}$

4.  $\frac{1}{\mathrm{\pi f}\left(2\mathrm{\pi f} L + R\right)}$

A coil of inductive reactance 31 $\mathrm{\Omega }$ has a resistance of 8 $\mathrm{\Omega }$. It is placed in series with a condenser of capacity reactance 25 $\mathrm{\Omega }$. The combination is connected to an AC source of 110 V. The power factor of the circuit is

1.  0.56

2.  0.64

3.  0.80

4.  0.33

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