An electric lamp connected in series with a capacitor and an $A.C.$ source is glowing with a certain brightness. On increasing the value of capacitance,the brightness of the lamp

$A$ $20 V$ $AC$ is applied to a circuit consisting of a resistor and a coil with negligible resistance. If the voltage across the resistor is $12 V$,the voltage across the coil is (in $V$)

When an inductor $L$ and a resistor $R$ in series are connected across a $15 \, V, 50 \, Hz$ a.c. supply, a current of $0.3 \, A$ flows in the circuit. The current differs in phase from the applied voltage by $(\frac{\pi}{3})^c$. The value of $R$ is:
$(\sin \frac{\pi}{6} = \cos \frac{\pi}{3} = \frac{1}{2}, \sin \frac{\pi}{3} = \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2})$

$A$ coil having an inductance of $\frac{1}{\pi} \text{ H}$ is connected in series with a resistance of $300 \text{ } \Omega$. If an $A$.$C$. source $(20 \text{ V}, 200 \text{ Hz})$ is connected across the combination,the phase angle between voltage and current is

The given figure represents the phasor diagram of a series $LCR$ circuit connected to an $ac$ source. At the instant $t'$ when the source voltage is given by $V = V_0 \cos(\omega t')$,the current in the circuit will be:
Given: $V_{OL} = 3 \text{ V}$,$V_{OR} = \sqrt{3} \text{ V}$,$V_{OC} = 2 \text{ V}$.

Two resistors are connected in series across a $5\,V\,rms$ source of alternating potential. The potential difference across the $6\,\Omega$ resistor is $3\,V$. If $R$ is replaced by a pure inductor $L$ of such magnitude that the current remains the same,then the potential difference across $L$ is.......$V$.