Question

The magnetic flux that passes through one turn of a 26-turn coil of wire changes to 4.5 Wb from 12.0 Wb in a time of 0.034 s. The average induced current in the coil is 150 A. What is the resistance of the wire?

Answer 1

Answer:

The resistance of the wire is 1.47 ohms

Explanation:

Electromagnetic induction is a physical phenomenon that consists on generate electric current changing magnetic flux. The magnitude of the electromotive force (emf) generated by the change on magnetic flux is given by Faraday-Lenz law:

$\xi=N\mid \frac{d\varphi_{B}}{dt} \mid$

with N the turns of the coil, and phi_{B} the magnetic flux.

So, in our case because the magnetic flux changes from 12.0 Wb to 4.5 Wb on 0.034 seconds.

$\xi=25\mid \frac{4.5 - 12.0}{0.034} \mid =220.59 V$

The electromotive force acts as voltage source for the coil, so we can use Ohm's law:

$V=IR$

with I the current, R the resistance and V the voltage (the emf), solving for R

$R=\frac{\xi}{I}= \frac{220.59}{150}$

$R=1.47 \Omega$