$A$ series $LCR$ circuit has $L=0.01\,H$,$R=10\,\Omega$,and $C=1\,\mu F$ and it is connected to an $AC$ voltage of amplitude $V_m = 50\,V$. At a frequency $60\%$ lower than the resonant frequency,the amplitude of the current will be approximately $...............\,mA$.

At very high frequencies,the effective impedance of the given circuit will be $.... \Omega$.

In an $LCR$ series circuit,when $L$ is removed from the circuit,the phase difference between voltage and current is $\frac{\pi}{3}$. If $C$ is removed from the circuit instead of $L$,the phase difference is again $\frac{\pi}{3}$. The power factor of the circuit is $(\tan 60^{\circ}=\sqrt{3})$.

$A$ direct current of $10 \,A$ is superimposed on an alternating current $I = 40 \cos \omega t \; (A)$ flowing through a wire. The effective value of the resulting current will be ....... $A$.

The power is transmitted from a power house on high voltage $ac$ because

$A$ steady current of magnitude $I$ and an $AC$ current of peak value $I$ are allowed to pass through identical resistors for the same time. The ratio of heat produced in the two resistors will be