Phasors and Phasor Diagrams

Question

A series R-C circuit is connected to an alternating voltage source. Consider two situations:

(a) When capacitor is air filled.

(b) When capacitor is mica filled. Current through resistor is i and voltage across capacitor is V then

Moderate

Solution

$\text{Current through resistor,}i$

$=\text{Current in the circuit}$

$=\frac{{V}_{0}}{\sqrt{{R}^{2}+{X}_{C}^{2}}}=\frac{{V}_{0}}{\sqrt{{R}^{2}+(1/\omega C{)}^{2}}}$

$\text{Voltage across capacitor,}V=i{X}_{C}$

$=\frac{{V}_{0}}{\sqrt{{R}^{2}+(1/\omega C{)}^{2}}}\times \frac{1}{\omega C}=\frac{{V}_{0}}{\sqrt{{R}^{2}{\omega}^{2}{C}^{2}+1}}$

$\text{As}{C}_{a}{C}_{b}$

$\therefore {i}_{a}{i}_{b}\text{and}{V}_{a}{V}_{b}$

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