1 mue F capacitor is connected to 220v 50hz ac source calculate the RMS value of current through circuit also find peak value of voltage across a capacitor?

Question

Answer

Z = Xc = 1/(2πfC) = 3185 ohm
Vrms = Irms × Z
Irms = Vrms / Z = 220V / 3185ohm
Irms = 0.069A = 69mA
Irms = 0.707Ip
Ip = 69mA /0.707 = 97.59mA ~ 97.6mA

Answer

Calculations for RMS Current and Peak Voltage
- First, we need to calculate the impedance of the capacitor in the circuit. Impedance of a capacitor is given by the formula Zc = 1 / (2 * π * f * C), where f is the frequency in Hz and C is the capacitance in Farads.
- Plugging in the values, Zc = 1 / (2 * π * 50 * 1 x 10^-6) = 3183.1 ohms.

RMS Current Calculation:
- The RMS current through the circuit can be calculated using Ohm's Law, Irms = Vrms / Zc, where Vrms is the RMS voltage across the capacitor.
- Given that Vrms = 220V, Irms = 220 / 3183.1 = 0.069 A or 69 mA.

Peak Voltage Calculation:
- The peak voltage across the capacitor can be calculated using the formula Vpeak = √2 * Vrms, where Vrms is the RMS voltage.
- Vpeak = √2 * 220 = 311.1 V.
Therefore, the RMS value of current through the circuit is 69 mA and the peak value of voltage across the capacitor is 311.1 V. These calculations are essential in understanding the behavior of the circuit and ensuring proper functioning of the components involved.

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