In a series $LCR$ circuit,the resistance is $18 \ \Omega$ and the impedance is $33 \ \Omega$. An $r.m.s.$ voltage of $220 \ V$ is applied across the circuit. The true power consumed in the $a.c.$ circuit is: (in $W$)

When a capacitor is connected in series with an $LR$ circuit,the alternating current flowing in the circuit

Draw phasor diagrams for $X_C > X_L$ and $X_C < X_L$,and state the disadvantages of the phasor method.

$A$ 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.

The value of alternating e.m.f. $(E)$ in the given circuit is (in $V$)

$A$ circuit has three elements: a resistance of $11 \Omega$,a coil of inductive reactance $120 \Omega$,and a capacitive reactance of $120 \Omega$ in series,connected to an $A.C.$ source of $110 \, V, 60 \, Hz$. Which of the three elements has the minimum potential difference?