An AC power supply has a rms voltage of 47.0 V. It is connected in series with a 340 Ωresistor, a 650 mH inductor, and an 8.4 μF capacitor. It’s found that the total voltage is ahead of the current by 35°. What is the frequency of the power supply?

The frequency of the power supply is f=68.49HZ

Explanation:

From the given question

We begin by understanding what circuit we are dealing with, off course it's an RLC circuit

Given data

Rms voltage =47volts

Resistance R=340ohms

Capacitance C =8.4*10^-6F

Inductance L= 650*10^-3H

But in RLC circuit resonance frequency F occurs when the capacitive reactance equals the inductive reactance

At resonance f

2*pi*f*L=1/2(pi*C)

f=1/2*pi√L*C

Substituting our values we have

f=1/(2*3.142√650*10^-3*8.4*10^-6)

f=1/(2*3.142√5460*10^-9)

f=1/6.284*0.00233

f=1/0.0146

f=68.49HZ

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y