Given that the current \(i_1=3A \sin \omega t\) and the current \(i_2=4A \cos \omega t,\) what will be the expression for the current \(i_3\)?

                  
1. \(5 A \sin \left(\omega t+53^{\circ}\right) \)
2. \(5 A \sin \left(\omega t+37^{\circ}\right) \)
3. \(5 A \sin \left(\omega t+45^{\circ}\right) \)
4. \( 5 A \sin \left(\omega t+30^{\circ}\right)\)

A capacitor of capacitance \(1~\mu\text{F}\) is charged to a potential of \(1\) V. It is connected in parallel to an inductor of inductance \(10^{-3}~\text{H}\). What is the value of the maximum current that will flow in the circuit?
1. \(\sqrt{1000}~\text{mA}\)
2. \(1~\text{mA}\)
3. \(1~\mu\text{F}\)
4. \(1000~\text{mA}\)

In a box \(Z\) of unknown elements (\(L\) or \(R\) or any other combination), an ac voltage \(E = E_0 \sin(\omega t + \phi)\) $$is applied and the current in the circuit is found to be \(I = I_0 \sin\left(\omega t + \phi +\frac{\pi}{4}\right)\). The unknown elements in the box could be:
             

In the transformer shown in the figure, the ratio of the number of turns of primary to the secondary is $\frac{N_1}{N_2}=\frac{1}{50}$. If a battery of emf 10 V is connected across primary, then induced current through the load of 10 k$\Omega$ in the secondary is

$1. \frac{1}{20}A$
$2. Zero$
$3. \frac{1}{10}A$
$4. \frac{1}{5}A$

EMF induced in the secondary coil of an ideal transformer does not depend upon

1. EMF in the primary coil

2. Frequency of source

3. Ratio of number of turns

4. Both (1) & (3)

The phase difference between emf and current through the choke coil maybe

1. 0$°$

2. 85$°$

3. 45$°$

4. 30$°$

The value of current in two series LCR circuit at resonance is the same when connected across a sinusoidal voltage source. Then

1. Both circuit should have the same value of capacitance and inductor

2. In both circuits, the ratio of L and C will be the same

3. For both the circuits, resistance must be the same

4. Both circuit should have the same impedance at all frequencies

An ideal transformer is made to step down the power line voltage of 2200 V for distribution to a city at 220 v. If the full load impedance of the city is 4 $\Omega$ then the primary current is

1. 45 A

2. 5.5 A

3. 55 A

4. 0.55 A