In an $LR$-circuit,the inductive reactance is equal to the resistance $R$. If the applied voltage is $E = E_0 \cos(\omega t)$,what is the power dissipated in the circuit?

$A$ resistor of $200 \; \Omega$ and a capacitor of $15.0 \; \mu F$ are connected in series to a $220 \; V, 50 \; Hz$ $ac$ source.
$(a)$ Calculate the current in the circuit.
$(b)$ Calculate the voltage $(rms)$ across the resistor and the capacitor. Is the algebraic sum of these voltages more than the source voltage? If yes,resolve the paradox.

When $100 \, V$ $DC$ is applied across a coil,a current of $1 \, A$ flows through it. When $100 \, V$ $AC$ at $50 \, Hz$ is applied to the same coil,only $0.5 \, A$ current flows. The impedance of the coil is ....... $\Omega$.

$A$ coil of inductance $0.1 H$ and resistance $110 \Omega$ is connected to a source of $110 V$ and $350 Hz$. The phase difference between the voltage maximum and the current maximum is

In an $LCR$ series circuit, an alternating voltage source of frequency $F$ is connected. The current leads the voltage by $45^{\circ}$. The value of $L$ is

An a.c. source of $15 \, V, 50 \, Hz$ is connected across an inductor $(L)$ and resistance $(R)$ in series. The $R.M.S.$ current of $0.5 \, A$ flows in the circuit. The phase difference between the applied voltage and current is $\left(\frac{\pi}{3}\right)$ radian. The value of resistance $(R)$ is $\left(\tan 60^{\circ}=\sqrt{3}\right)$. (in $\Omega$)