Question

An ac generator has a maximum emf output of 155 v.

Answer 1

Vp = 155 V
R = 53 ω

(a) RMS emf output

Vrms = 0.7071Vp = 0.7071*155 = 109.6 V

(b) RMS current
From ohm's law,
Vrms = IrmsR => Irms = Vrms/R = 109.6/53 = 2.07 Amps

Answer 2

A) For an ac generator, the rms value of the voltage is given by:
$V_{rms} = \frac{V_0}{ \sqrt{2} }$
where $V_0$ is the peak value of the voltage.

For the generator in our problem, the peak value is $V_0=155 V$, therefore the rms value of the voltage is
$V_{rms}= \frac{V_0}{ \sqrt{2} }= \frac{155 V}{ \sqrt{2} }=109.6 V$


b) We can find the rms current in the circuit by using Ohm's law, which is also valid when using the rms values of the current and the voltage:
$I_{rms} = \frac{V_{rms}}{R}$
where R is the resistance conncected to generator. If we use $R=53 \Omega$, we find
$I_{rms} = \frac{V_{rms}}{ R }= \frac{109.6 V}{53 \Omega} =2.07 A$