# Single Phase Circuit

A resistor and a capacitor are connected in series across a 150 V a.c supply. When the frequency is 40 Hz the current is 5 A, and when the frequency is 50 Hz the current is 6 A. Find the resistance and capacitance of the resistor and capacitor respectively.

If they are now connected in parallel across the 150 V supply, find the total current and its power factor when the frequency is 50 Hz.

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#### Solution Preview

A resistor and a capacitor are connected in series across a 150 V a.c supply. When the frequency is 40 Hz the current is 5 A, and when the frequency is 50 Hz the current is 6 A. Find the resistance and capacitance of the resistor and capacitor respectively.

If they are now connected in parallel across the 150 V supply, find the total current and its power factor when the frequency is 50 Hz.

Solution: R C

I

V = VosinÏ‰t = Vosin2Î ft

Part I

Case 1: Frequency f = 40 Hz, Angular frequency = Ï‰ = 2Î f = 2Î x 40 = 251.33 rad/sec

Reactance of the capacitor = XC = 1/jÏ‰C = 1/j(251.33C)

Impedance of the R-C series combination = Z = R + XC = R + 1/j(251.33C) = R - j ...

#### Solution Summary

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