In a series $R$ $-$ $C$ circuit shown in figure, the applied voltage is $10\, V$ and the voltage across capacitor is found to be $8 \,V$. Then, the voltage across $R$ and the phase difference between current and the applied voltage will respectively be

An $LC$ circuit consists of a capacitor and a coil with a large number of turns. Suppose all the linear dimensions of all elements of the circuit are increased by a factor of $2$ while keeping the number of turns on the coil constant. How much does the resonant frequency of the circuit change?

Let $f = 50\, Hz$, and $C = 100\, \mu\, F$ in an $AC$ circuit containing a capicator only. If the peak value of the current in the circuit is $1.57$ $A$ at $t = 0$. The expression for the instantaneous voltage across the capacitor will be

$A$ circuit element is placed in a closed box. At time $t=0$, constant current generator supplying a current of $1\, amp$, is connected across the box. Potential difference across the box varies according to graph shown in figure. The element in the box is :

In a series $L R$ circuit $X_{L}=R$ and power factor of the circuit is $P _{1}$. When capacitor with capacitance $C$ such that $X _{ L }= X _{ C }$ is put in series, the power factor becomes $P_{2}$. The ratio $\frac{ P _{1}}{ P _{2}}$ is