First slide

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

A

$i_{a} > i_{b}$
B

$V_{a} = V_{b}$
C

$V_{a} < V_{b}$
D

$V_{a} > V_{b}$

Solution

$Current through resistor, i$

$= Current in the circuit$
$= \frac{V_{0}}{\sqrt{R^{2} + X_{C}^{2}}} = \frac{V_{0}}{\sqrt{R^{2} + (1 / ω C)^{2}}}$
$Voltage across capacitor, V = i X_{C}$
$= \frac{V_{0}}{\sqrt{R^{2} + (1 / ω C)^{2}}} \times \frac{1}{ω C} = \frac{V_{0}}{\sqrt{R^{2} ω^{2} C^{2} + 1}}$
$As C_{a} < C_{b}$
$∴ i_{a} < i_{b} and V_{a} > V_{b}$

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