Find RMS value of current flowing through a 314 μF capacitor when connected to 230 V, 50 Hz, single phase AC supply. Write the equation of instantaneous voltage and current.

Q.1 (b) Find RMS value of current flowing through a 314 μF capacitor when connected to 230 V, 50 Hz, single phase AC supply. Write the equation of instantaneous voltage and current.

Doubtly Asked 25 Oct 2026 mu engineering Save WhatsApp Report

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\( X_C = \dfrac{1}{2\pi fC} = \dfrac{1}{2\pi\times50\times314\times10^{-6}} = \dfrac{1}{0.09865} = 10.14\ \Omega \).

RMS current: \( I = \dfrac{V}{X_C} = \dfrac{230}{10.14} = \) 22.69 A.

V_m = 230√2 = 325.27 V; I_m = 22.69√2 = 32.09 A; ω = 314.16 rad/s. In a pure capacitor the current leads the voltage by 90°:

v = 325.27 sin(314.16 t) V; i = 32.09 sin(314.16 t + 90°) A = 32.09 sin(314.16 t + π/2) A.

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report

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Find RMS value of current flowing through a 314 μF capacitor when connected to 230 V, 50 Hz, single phase AC supply. Write the equation of instantaneous voltage and current.

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