$A$ resistor and a capacitor are connected in series with an $AC$ source. If the potential drop across the capacitor is $5 \,V$ and that across the resistor is $12 \,V$, then the applied voltage is (in $\,V$)

An $AC$ circuit has an inductor and a resistor of resistance $R$ in series,such that $X_L = 3R$. Now,a capacitor is added in series such that $X_C = 2R$. The ratio of the new power factor to the old power factor of the circuit is $\sqrt{5} : x$. The value of $x$ is ...... .

In a series $L-C-R$ circuit,

In an $RC$ $AC$ circuit,the maximum voltage and maximum current are $100 \ V$ and $1.1 \ A$ respectively. If $X_{C} = 60 \ \Omega$ and $R = 80 \ \Omega$,then the power consumed in the circuit will be . . . . . . . (in $W$)

$A$ student connects a long air-cored coil of manganin wire to a $100 \ V$ $DC$ supply and records a current of $25 \ A$. When the same coil is connected across a $100 \ V, 50 \ Hz$ $AC$ supply,the current reduces to $20 \ A$. The reactance of the coil is $...... \Omega$.

In a simple $L-R$ circuit with an $A.C.$ source,the potential difference at any instant across the inductor and the resistor are $V_L$ and $V_R$ respectively,and the $A.C.$ source has a potential difference $V_{AC}$ at the same instant. Then: