Q.A series L-C-R circuit is connected to AC source. Using the phasor diagram, derive the expression for the impedance of the circuit. OR The instantaneous current and voltage of an AC circuit are given by I = 10 sin(314t) A and V = 200 sin(314t) V. What is the average power dissipation over a complete cycle in the circuit?

Using a phasor (rotating vector) diagram, the voltages across R, L and C add vectorially (since they are out of phase with the common current) to give $Z=\sqrt{R^2+(X_L-X_C)^2}$.

In a series L-C-R circuit connected to an AC source, the same current $I = I_0\sin\omega t$ flows through all three elements, so current is taken as the reference phasor.

• Voltage across $R$: $V_R = IR$, in phase with $I$ (phasor along the current direction).
• Voltage across $L$: $V_L = IX_L$, leads $I$ by $90°$ (phasor drawn $90°$ ahead).
• Voltage across $C$: $V_C = IX_C$, lags $I$ by $90°$ (phasor drawn $90°$ behind).

Since $V_L$ and $V_C$ are along the same line but opposite directions (both perpendicular to $I$, one up one down), their resultant is $(V_L - V_C)$, perpendicular to $V_R$.

By the phasor (vector) diagram, the resultant applied voltage is the vector sum: …