An ac source of 50V (r.m.s value) is connected across a series R-C circuit. If the r.m.s voltage across the resistor is 40V , then the r.m.s voltage across the capacitor is

Question

An ac source of 50V (r.m.s value) is connected across a series R-C circuit. If the r.m.s voltage across the resistor is 40V , then the r.m.s voltage across the capacitor is (A) 10V (B) 20V (C) 30V (D) 40V

Tardigrade Admin · Accepted Answer

For an R - C circuit Applied voltage, V=√VR2 + VC2 , where VR &VC represents voltage across resistance and voltage across capacitor. ∴ 50=√(40)2 + VC2 ⇒ VC=30 V

Q. An ac source of $50 V$ (r.m.s value) is connected across a series $R - C$ circuit. If the r.m.s voltage across the resistor is $40 V$ , then the r.m.s voltage across the capacitor is

$10 V$

$20 V$

$30 V$

$40 V$

For an R - C circuit
Applied voltage, $V = V_{R}^{2} + V_{C}^{2}$ , where $V_{R} & V_{C}$ represents voltage across resistance and voltage across capacitor.
$∴ 50 = (40)^{2} + V_{C}^{2}$
$\Rightarrow V_{C} = 30 V$

Q. An ac source of 50V (r.m.s value) is connected across a series R−C circuit. If the r.m.s voltage across the resistor is 40V , then the r.m.s voltage across the capacitor is

10V

20V

30V

40V