Chapter 21, Problem 25P

To determine

The current in the motor if the load causes it to run at half speed.

Answer to Problem 25P

Solution:

If the motor runs at half speed, current in the motor is $\text{13}\text{.2 A}$

Explanation of Solution

Given info:

The full speed against its normal load =108v [As per example 21-8]

Resistance=$\text{5Ώ}$

Emf=$\text{120 V}$ [As per example 21-8 ]

If the load causes it to run at half speed=$\text{54 V}$

Because, the greater the speed of the motor,the greater the back emf. Thus, if the load causes it to run at half speed, then the back emf is half as it proportional to the rotation of speed.

From the equation of induced backup emf (to find the new current)

${\text{E-E}}_{\text{back}}\text{-IR = 0}$

$\Rightarrow \text{I=}\frac{{\text{E-E}}_{\text{back}}}{\text{R}}$

$=\frac{120-54}{5}$

$\text{= 13}\text{.2 A}$