Question

A generator consists of a rectangular loop with turns of wire spinning at in a uniform magnetic field. The generator output is connected to a series RC circuit consisting of a and a capacitor. What is the average power delivered to the circuit?

Answer 1

Full question:

A generator consists of a 18-cm by 12-cm rectangular loop with 500 turns of wire spinning at 60 Hz in a 25 mT uniform magnetic field. The generator output is connected to a series RC circuit consisting of a 150 Ω and a 35 μF capacitor.What is the average power delivered to the circuit?

Answer:

The average power delivered to the circiut is 27.5 W

Solution:

Induced emf amplitude = N A B w  

N- Number of turns of the coil

B- Magnetic field

$=500 \times(0.18 \times 0.12) \times 0.025 \times(2 \pi 60)$

Induced emf amplitude = 101.8 Volt

$\begin{aligned}&X_{c}=\frac{1}{(2 p i f C)}=\frac{1}{2 \times \pi \times 60 \times 35 \times 10^{-6}}\\&X_{c}=75.8\ \mathrm{ohm}\end{aligned}$

R = 150 ohm

$\begin{aligned}&z=\sqrt{\left[R^{2}+X_{c}^{2}\right]}=168 \text { ohm }\\&I_{\text {peak}}=\frac{101.8}{168}=0.606\ \mathrm{A}\\&P_{a v g}=\frac{l^{2} R}{2}=27.5\ \mathrm{W}\end{aligned}$