An alternating power supply of $220 \,V$ is applied across a series circuit of resistance $10 \sqrt{3} \,\Omega$,capacitive reactance $40 \,\Omega$,and inductive reactance $30 \,\Omega$. The respective currents in the circuit for zero and infinite frequencies are

$A$ bulb is connected first with $DC$ and then $AC$ of the same voltage. In which case will it shine more brightly?

Assertion : In the purely resistive element of a series $LCR$ $AC$ circuit,the maximum value of $rms$ current increases with an increase in the angular frequency of the applied $e.m.f$.
Reason : $I_{\max} = \frac{\varepsilon_{\max}}{Z}$,where $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$ and $I_{\max}$ is the peak current in a cycle.

In an $LCR$ circuit $R = 100 \ \Omega$. When capacitance $C$ is removed,the current lags behind the voltage by $\pi /3$. When inductance $L$ is removed,the current leads the voltage by $\pi /3$. The impedance of the circuit is......$\Omega$.

If $C, R, L$ and $I$ denote capacity, resistance, inductance and electric current respectively, the quantities having the same dimensions of time are :
$(1)$ $C R$
$(2)$ $\frac{L}{R}$
$(3)$ $\sqrt{L C}$
$(4)$ $L I^2$

In the circuit shown in the figure, neglecting the source resistance, the voltmeter and ammeter readings respectively are