In an $L-R$ circuit,the value of $L$ is $(\frac{0.4}{\pi}) \, H$ and the value of $R$ is $30 \, \Omega$. If an alternating e.m.f. of $200 \, V$ at $50 \, Hz$ is connected to the circuit,what are the impedance and the current in the circuit?

The $LC$ series resonant circuit produces a resonant frequency '$f$'. If $L$ is tripled and $C$ is increased by $3C$, the resonant frequency will be

For a series $LCR$ circuit with $R=100\,\Omega$,$L=0.5\,mH$ and $C=0.1\,pF$ connected across $220\,V-50\,Hz$ $AC$ supply,the phase angle between current and supplied voltage and the nature of the circuit is:

In a circuit,a metal filament lamp is connected in series with a capacitor of capacitance $C \mu F$ across a $200 V, 50 Hz$ supply. The power consumed by the lamp is $500 W$ while the voltage drop across it is $100 V$. Assume that there is no inductive load in the circuit. Take $rms$ values of the voltages. The magnitude of the phase-angle (in degrees) between the current and the supply voltage is $\varphi$.
Assume,$\pi \sqrt{3} \approx 5$.
$(1)$ The value of $C$ is . . . . . .
$(2)$ The value of $\varphi$ is
Give the answers of the questions $(1)$ and $(2)$:

When an inductor $L$ and a resistor $R$ in series are connected across a $12 \, V, 50 \, Hz$ supply, a current of $0.5 \, A$ flows in the circuit. The current differs in phase from the applied voltage by $\frac{\pi}{3}$ radian. Then the value of $R$ is (in $\Omega$)

In the figure,if $A$ and $B$ are identical bulbs,which bulb glows brighter?