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

1.	10 mH
2.	100 mH
3.	1 mH
4.	Cannot be calculated unless R is known

A 50 Hz a.c. source of 20 volts is connected across R and C as shown in the figure below. If the voltage across R is 12 volts, then the voltage across C will be:
   

Alternating current cannot be measured by a D.C. ammeter because:

In an L-R circuit, the inductive reactance is equal to the resistance R of the circuit. An emf of E = E₀cos(ωt) is applied to the circuit. The power consumed by the circuit is:

1. $\frac{{\mathrm{E}}_0^2}{\sqrt{2}\mathrm{R}}$

2. $\frac{{\mathrm{E}}_0^2}{4\mathrm{R}}$

3. $\frac{{\mathrm{E}}_0^2}{2\mathrm{R}}$

4. $\frac{{\mathrm{E}}_0^2}{8\mathrm{R}}$

A series AC circuit has a resistance of 4 $\mathrm{\Omega }$ and an inductor of reactance 3 $\mathrm{\Omega }$. The impedance of the circuit is z₁. Now when a capacitor of reactance 6 $\mathrm{\Omega }$ is connected in series with the above combination, the impedance becomes $z_{2.}$ $\frac{{\mathrm{z}}_1}{{\mathrm{z}}_2}$ will be:

1. 1 : 1

2. 5 : 4

3. 4 : 5

4. 2 : 1

An inductor of \(20~\text{mH}\), a capacitor of \(100~\mu \text{F}\), and a resistor of \(50~\Omega\) are connected in series across a source of emf, \(V=10 \sin (314 t)\). What is the power loss in this circuit?
1. \( 0.79 ~\text{W} \)
2. \( 0.43 ~\text{W} \)
3. \( 2.74 ~\text{W} \)
4. \( 1.13 ~\text{W}\)

An inductor (L) and resistance (R) are connected in series with  an AC source. The phase difference between voltage (V) and current (i) is $45°$. If the phase difference between V and i remains the same, then the capacitive reactance and impedance of the L-C-R circuit will be:

1. 2R, R$\sqrt{2}$

2. R, R$\sqrt{2}$

3. R, R

4. 2R, R$\sqrt{3}$

A transformer has an efficiency of 90% when working on a 200 V and 3 kW power supply. If the current in the secondary coil is 6 A, the voltage across the secondary coil and the current in the primary coil, respectively, are:

1. 300 V, 15 A

2. 450 V, 15 A

3. 450 V, 13.5 A

4. 600 V, 15 A

The core of a transformer is laminated because:

How much power is dissipated in an \(\mathrm{L-C-R}\) series circuit connected to an \(\mathrm{AC}\) source of emf \(\mathrm E\)?