A transformer is used to light a \(100~\text{W}\) and \(110~\text{V}\) lamp from a \(220~\text{V}\) main. If the main current is \(0.5~\text{A}\), the efficiency of the transformer is approximately:
1. \(30\%\)
2. \(50\%\)
3. \(90\%\)
4. \(10\%\)

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. \(f/2\)

The core of a transformer is laminated so that:

A coil of inductive reactance \(31~\Omega\) has a resistance of
\(8~\Omega\). It is placed in series with a condenser of capacitive reactance \(25~\Omega\). The combination is connected to an a.c. source of
\(110~\text{V}\). 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 μF and ω=1000 s^-1?

1. 100 mH

2. 1 mH

3. cannot be calculated unless R is known

4. 10 mH

In an AC circuit, the emf (e) and the current (I) at any instant are given respectively by 
e = E₀sin$\mathrm{\omega }$t 
I = I₀sin$\left(\mathrm{\omega t}-\mathrm{\varphi }\right)$ 
The average power in the circuit over one cycle of AC is:

1.  $\frac{{\mathrm{E}}_{\mathrm{o}}{\mathrm{I}}_{\mathrm{o}}}{2}$

2.  $\frac{{\mathrm{E}}_{\mathrm{o}}{\mathrm{I}}_{\mathrm{o}}}{2}$ $\sin$ $\mathrm{\varphi }$

3.  $\frac{{\mathrm{E}}_{\mathrm{o}}{\mathrm{I}}_{\mathrm{o}}}{2}$ $\cos$ $\mathrm{\varphi }$

4.  ${\mathrm{E}}_{\mathrm{o}}{\mathrm{I}}_{\mathrm{o}}$

The power dissipated in an L-C-R series circuit connected to an AC source of emf E is:

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. \(3.6\) A
2. \(2.8\) A
3. \(2.5\) A
4. \(5.0\) A

In the given circuit, the reading of voltmeter V₁ and V₂ are 300 V each. The reading of the voltmeter V₃ and ammeter A are respectively:

1. 150 V, 2.2 A

2. 220 V, 2.2 A

3. 220 V, 2.0 A

4. 100 V, 2.0 A

An AC voltage is applied to a resistance R and an 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.  $\frac{\mathrm{\pi }}{4}$

2.  $\frac{\mathrm{\pi }}{2}$

3.  zero

4.  $\frac{\mathrm{\pi }}{6}$