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A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz . (a) What is the phase angleϕfor the source voltage relative to the current? Does the source voltage lag or lead the current? (b) What is the capacitance C of the capacitor if the current amplitude is 5.30 A?

Short Answer

Expert verified

The phase angle ϕfor the source voltage relative to the current is 90°and voltage lags the current. The capacitance C = 1.75×10-4F.

Step by step solution

01

Step-1: Formulas used  

ϕis the phase angle, the difference in the voltage and current phases.

For ac source connected with a capacitor, the capacitive reactance in the circuit is given by equation in the form

Xc=VI

Also, this capacitive reactance is related to the frequency and the capacitance C of the capacitor in the form

Xc=12ττfC

Both equations have the same right sides, so we can get an expression for the capacitance C by

VI=12ττfC, then

C=I2ττfV

02

Step-2: Calculation for capacitance C

Plug in the values for V, I and f to get value of C

C=5.3A2ττ80Hz60V=1.75×10-4F

The capacitor store charges and this makes the voltage lags the current and this process is opposite to the coil. So, the phase angle ϕ will be in negative sign and equals 90°

Therefore the phase angle ϕfor the source voltage relative to the current is -90°and voltage lags the current. The capacitance C = 1.75×10-4F.

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