It is found that the current through the \(LCR\) series circuit is at its maximum. If \(V_r, V_C~\text{and}~V_L\) are potential differences across resistance, capacitor, and inductor respectively, then which of the following is correct?

1.	\(V_r=V_L>V_C\)
2.	\(V_R \neq V_L=V_C\)
3.	\(V_R \neq V_L \neq V_C\)
4.	\(V_R=V_C \neq V_L\)

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:
             

What is the value of the power factor for a parallel LC circuit at a frequency less than the resonance frequency?

1. Zero

2. 1

3. > 1

4.< 1

When an alternating voltage is given as \(E = (6 \sin\omega t - 2 \cos \omega t)\) volt, what is its rms value?
1. \(4 \sqrt 2 \) V
2. \(2 \sqrt 5\) V
3. \(2 \sqrt 3\) V
4. \(4\) V

An LC circuit contains an inductor (L=25 mH) and a capacitor (C=25 mF) with an initial charge of Q₀. At what time will the circuit have an equal amount of electrical and magnetic energy?

$1.$ $\frac{\mathrm{\pi }}{\mathrm{160 }}s$

$2.$ $\frac{3\mathrm{\pi }}{\mathrm{160 }}s$

$3.$ $\frac{5\mathrm{\pi }}{\mathrm{160 }}s$

4. All of these

In which of the following circuits can the power factor be zero?

1. LC circuit

2. LCR circuit

3. Purely resistive circuit

4. Both (1) & (2)