A resistor of 200 ohm and a capacitor of 15micro farad are connected in series to a 220v ,50hz ac source.Calculate the current in the circuit and the rms voltage across the resistor and the capacitor.Is the algebraic sum of these voltages more than the source voltage

A resistor of 200 ohm and a capacitor of 15micro farad are connected i

1.	A resistor of 200 ohm and a capacitor of 15micro farad are connected in series to a 220v ,50hz ac source.Calculate the current in the circuit and the rms voltage across the resistor and the capacitor.Is the algebraic sum of these voltages more than the source voltage
Answer» Given that R = 200Ω C = 15 μF = 15 × 10–6 F ξ = ξ sinωt ξ = 220 V f = 50 Hz W = 2πf = (100π) rad/s ξ = 220 sin (100π) REACTANCE of capacitor Xc = 1/ We = 1 / 100 * pi * 15 * 10^-6 = 10^6 / 314 * 15 = 212.31 ohm So, impedance Z = sqrt (R^2 + X^2) Z = sqrt (200^2 + 212.31^2) = 291.67 ohm I = E / Z = 220 sin (100* pi * t) / 291.67 = 0.75 sin (100 * pi *t) Irms = 0.75A Voltage across capacitor VR = Irms × XC = 0.75 × 200 = 150 volt Voltage across capacitor VC = Irms × XC = 0.75 × 212.31 = 159.23 volt

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A resistor of 200 ohm and a capacitor of 15micro farad are connected in series to a 220v ,50hz ac source.Calculate the current in the circuit and the rms voltage across the resistor and the capacitor.Is the algebraic sum of these voltages more than the source voltage

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