Question

A resistor of $200\Omega$ and a capacitor of $40\mu F$ are connected in series to 220 V AC source with angular frequency $\left(\Omega \right)$ = 300 Hz. Calculate the voltage (rms) across the resistor and the capacitor why is the algebraic sum of these voltages more than the source voltage? How do you resolve this paradox?

Answer 1

$Z=\sqrt{R^2+{(X_C-X_L)}^2}=\sqrt{R^2+{X_C}^2}=\sqrt{{200}^2+\frac{1}{{(300\times 40\times {10}^{-6})}^2}}=216.67\Omega$

$I=\frac{V}{Z}=\frac{220}{216.67}=1.02A$

when voltage drops across the resistor $=IR=1.02\times 200=204V$

when voltage drops across the capacitor $I{X}_C=1.02\times \frac{1}{300\times 40\times {10}^{-6}}=85V$

total voltage drop $=204+85=289V$

kirchoffs voltage law is valid when we consider the instantaneous values of voltage

85V and 204V are the rms value of the voltage

hence when these values are added the resultant will be greater than the source voltage