In the given $A.C.$ circuit,the instantaneous currents through the inductor and capacitor are $0.8 \,A$ and $0.4 \,A$ respectively. The instantaneous current through the resistor is:

$A$ resistor of resistance $40 \Omega$,a capacitor of capacitive reactance $20 \Omega$,and an inductor of inductive reactance $50 \Omega$ are connected in series to an $ac$ source of $100 \ V$. The current through the circuit is (in $A$)

The $L-C-R$ circuit shown below is driven by an ideal $AC$ voltage source. At frequency $f=\frac{1}{2 \pi \sqrt{L C}}$,choose the correct statement.

$A$ sinusoidal voltage of peak value $283 \;V$ and frequency $50 \;Hz$ is applied to a series $LCR$ circuit in which $R = 3 \;\Omega, L = 25.48 \;mH,$ and $C = 796 \;\mu F.$ Find
$(a)$ the impedance of the circuit;
$(b)$ the phase difference between the voltage across the source and the current;
$(c)$ the power dissipated in the circuit; and
$(d)$ the power factor.

Two coils require $20 \ min$ and $60 \ min$ respectively to produce the same amount of heat energy when connected separately to the same source. If they are connected in parallel to the same source,the time required to produce the same amount of heat by the combination of coils will be . . . . . . $min$.

As shown in the figure,a series circuit connected across a $200\, V$,$60\, Hz$ line consists of a capacitor of capacitive reactance $30\,\Omega$,a non-inductive resistor of $44\,\Omega$,and a coil of inductive reactance $90\,\Omega$ and resistance $36\,\Omega$. The power dissipated in the coil is......$W$.