A transformer has an efficiency of \(90\%\) working on \(200~\text V\) and \(3~\text{kW}\) power supply. If the current in the secondary coil is \(6~\text A,\) the voltage across the secondary coil and the current in the primary coil, respectively, are:
1. \(300~\text V,~15~\text A\) 
2. \(450~\text V,~15~\text A\)
3. \(450~\text V,~13.5~\text A\)
4. \(600~\text V,~15~\text A\)

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 \(\tan^{-1}\sqrt{3}\). If instead, \(C\) is removed from the circuit, the phase difference is again \(\tan^{-1}\sqrt{3}\). The power factor of the circuit is:

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.  $\frac{\mathrm{\pi }}{6}$

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

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

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

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

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

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. \(10\%\)