First slide

Phasors and Phasor Diagrams

Question

In the given circuit , V_C = 50 V and $R = 50 Ω .$ The values of C and V_R are

Moderate

A

$3 .3 μF, 60 V$
B

$104 μF, 98 V$
C

$1 .6 μF, 30 V$
D

$2 μF, 60 V$

Solution

$V_{C}^{2} + V_{R}^{2} = V^{2}$
$50^{2} + V_{R}^{2} = V^{2}$
$V_{R}^{2} = 110^{2} - 50^{2}$
$V_{R} = \sqrt{110^{2} - 50^{2}}$
$V_{R} = \sqrt{160 \times 60} ≃ 98 V$
Then, $I_{R} = \frac{98}{50}$ A $(∴ R = 50 Ω)$
Also, $I = I_{R} = \frac{110}{\sqrt{R^{2} + X_{C}^{2}}} \Rightarrow \frac{98}{50} = \frac{110}{\sqrt{50^{2} + X_{C}^{2}}}$
Find X_C and then use $X_{c} = \frac{1}{ωC}$ to find C.
$C = 104 μ F$

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