Q.In a series LCR circuit, if resistance, inductive reactance and capacitive reactance are 3Ω, 8Ω and 4Ω respectively, calculate phase difference between voltage and current.

When a resistor R, inductor L and capacitor C are connected in series to an AC source, carrying a common current $i=i_0\sin\omega t$, each element's own voltage drop bears a different, fixed phase relationship to that current: $e_R=i_0R$ (in phase), $e_L=i_0X_L$ (leading by $\pi/2$), and $e_C=i_0X_C$ (lagging by $\pi/2$). Since $e_L$ and $e_C$ are exactly $180^\circ$ apart, they combine by simple subtraction into a single net reactive voltage phasor, $(e_L-e_C)$, perpendicular to $e_R$; combining this with $e_R$ by the Pythagorean rule for perpendicular phasors gives the resultant applied voltage $e_0=i_0\sqrt{R^2+(X_L-X_C)^2}$. …