Question

A generator consists of a $12cm$ by $16cm$rectangular loop with $500$ turns of wire spinning at $60Hz$z in a $25mT$uniform magnetic field. The generator output is connected to a series RC circuit consisting of a$120ohm$ resistor and a $35mF$ capacitor. What is the average power delivered to the circuit?

Short answer

The average power delivered to the circuit is :-

$P_{avg}=24$W

Step-by-step solution

Given information

We have been given that a generator consists of a $12cm$ by $16cm$rectangular loop with $500$ turns of wire spinning at $60Hz$ in a $25mT$uniform magnetic field. The generator output is connected to a $120ohm$series RC circuit consisting of a resistor and a $35mF$capacitor. We have to find the average power delivered to the circuit.

Simplification

The voltage and current is:

$I_{\mathrm{rms}}=\frac{{\epsilon }_{\mathrm{rms}}}{\sqrt{R^2+X_C^2}}$

${\epsilon }_o=NBA\omega$

$=90.48V$

To find the expression :

$P_{\mathrm{avg}}=I_{\mathrm{rms}}^{2}R$

$=\frac{{\epsilon }_o^{2}R}{2\left(R^2+(1/2\pi fC{)}^2\right)}$

$=\frac{(90.48\mathrm{V}{)}^2(120\Omega )}{2\left[(120\Omega {)}^2+{\left(1/2\pi (60\mathrm{Hz})\left(35\times {10}^{-6}\mathrm{F}\right)\right)}^2\right]}$

$=24W$