Chapter 21, Problem 24P

To determine

The back emf at $\text{2300 rpm}$

Answer to Problem 24P

Solution:

Back emf at $\text{2300 rpm}$ is $92\text{ V}$

Explanation of Solution

Given info:

$\begin{array}{l}\text{Back Emf}\left(E\right)=\text{72 V} \\ \text{First angular speed }\left({\omega }_1\right)\text{=1800 rpm }\\ \text{Second angular speed }\left({\omega }_2\right)\text{=2300 rpm}\end{array}$

According to equation $E\alpha \omega$$,$ where E is back emf and $\omega$ is angular speed, both are directly proportional to each other so that the quotient is constant.

Since, back emf, $E=NBA\omega$

$E=\text{K }\omega$ [K= $NBA$, K=constant]

Therefore, the equation changes into

$\frac{E_1}{{\omega }_1}=\frac{E_2}{{\omega }_2}$

$\Rightarrow E_2={\omega }_2\frac{E_1}{{\omega }_1}$

Applying values,

$E_2=\left(72\right)\frac{2300}{1800}$

$E_2=92\text{ V}$