The impedance of an $LR$ circuit with $L=\frac{60}{\pi} \text{ mH}$,$R=8 \Omega$ and frequency $f=50 \text{ Hz}$ is (in $\Omega$)

When a $DC$ voltage of $100 \, V$ is applied to an inductor, a $DC$ current of $5 \, A$ flows through it. When an $AC$ voltage of $200 \, V$ peak value is connected to the inductor, its inductive reactance is found to be $20\sqrt{3} \, \Omega$. The power dissipated in the circuit is . . . . . . $W$.

In an $LR$ circuit of $3 \text{ mH}$ inductance and $4 \text{ } \Omega$ resistance,an $\text{emf } E = 4 \cos(1000t) \text{ V}$ is applied. The amplitude of the current is:

In an $L-R$ circuit,the inductive reactance is equal to $\sqrt{3}$ times the resistance $R$ of the circuit. An e.m.f. $E = E_0 \sin(\omega t)$ is applied to the circuit. The power consumed in the circuit is:

An alternating emf is applied across a parallel combination of a resistance $R$,capacitance $C$ and an inductance $L$. If $I_R$,$I_L$,and $I_C$ are the currents through $R$,$L$,and $C$ respectively,then the diagram which correctly represents the phase relationship among $I_R$,$I_L$,$I_C$,and the source emf $E$ is:

In the given circuit,the $rms$ value of current $(I_{rms})$ through the resistor $R$ is: $..........\,A$