A resistance R and a capacitor C are connected in series to a source V = V₀ sin $ω$ t. Find :
(a) The peak value of the voltage across the (i) resistance and (ii) capacitor.
(b) The phase difference between the applied voltage and current. Which of them is ahead?

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Detailed Solution

Peak value of current
$\begin{array}{l} I_{0} = \frac{V_{0}}{Z} = \frac{V_{0}}{\sqrt{X_{c}^{2} + R^{2}}} \\ X_{c} = \frac{1}{ωC} \end{array}$
(i) $V_{R} = I_{0} R = \frac{V_{0} R}{\sqrt{X_{c}^{2} + R^{2}}}$
(ii) $V_{c} = I_{0} X_{c} = (\frac{V_{0}}{\sqrt{X_{C}^{2} + R^{3}}}) X_{c}$
(b) From phasor
$tanϕ = \frac{X_{c}}{R}$
Current leads the applied voltage by phase $ϕ$