Question

A wire of length L is wound into a square coil with 167 turns and used in a generator that operates at 60.0 Hz and 120 V rms value in a 0.041-T magnetic field. What is the length L of the wire used to construct the coil

Answer 1

Answer:

$171.43m$

Explanation:

First, define $emf$( electromotive force )-is the unit electric charge imparted by an energy source. In this case the generator.

The peak emf is:

$E_p_e_a_k=\sqrt2(E_m_a_x)$=$\sqrt(2\times 120V)=170V$

Substituting $w=2\pi f$ and the value for peaf $E$ gives:

Total length=$4\sqrt {\frac{NE_p_e_a_k}{Bw}$=$4\sqrt{\frac{167\times 170}{0.041T\times 2pi \times 60.0Hz}$

=$171.43m$

Hence, wire's length is 171.43m