# 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 = Vosinωt = Vosin2Πft

Part I

Case 1: Frequency f = 40 Hz, Angular frequency = ω = 2Πf = 2Π x 40 = 251.33 rad/sec

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

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

#### Solution Summary

This solution is provided within an attached Word document and clearly demonstrates how to solve this physics based problem. All calculations are included and diagrams also accompany this solution.