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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# By how many percent is the torque of a motor decreased if its permanent magnets lose 5.0% of their strength? (b) How many percent would the current need to be increased to return the torque to original values?

(a)The required percent of the decrease in the torque is 5%.

(b)The required percent of the increase in the current is 5.3%.

See the step by step solution

## Step 1: Definition of Torque.

Torque is a measurement of the force required to rotate an object around an axis. In linear kinematics, the force causes an object to accelerate; in angular kinematics, torque causes an object to accelerate. The torque can be estimated using the expression,

where the number of turns, ${\mathbf{N}}$, the current, ${\mathbf{I}}$, the area of the loop, ${\mathbf{A}}$ , and the inclination angle of the loop, ${\mathbf{\theta }}$.

## Step 2: Finding the percent of the torque of a motor decrease(a)

The magnetic field strength in the initial $\left({\mathrm{B}}_{\mathrm{initial}}\right)$and final $\left({\mathrm{B}}_{\mathrm{Final}}\right)$ conditions can be calculated as,${\mathrm{B}}_{\mathrm{Final}=}{\mathrm{B}}_{\mathrm{initial}}-5%{\mathrm{B}}_{\mathrm{initial}}\phantom{\rule{0ex}{0ex}}=0.95{\mathrm{B}}_{\mathrm{initial}}$

We will use equation (1) for the torque and compare the initial and the final torque, and respectively.

Now, let us calculate the torque using the above calculation for magnetic field strength, we will get,

To get the decrease in the torque, we will subtract the final torque from the initial torque.

So, the decrease in the torque is.

## Step 3: Finding the percent that the current need to be increased to return the torque to the original values(b)

In this case, the value of the initial torque is the same as the final torque. We will compare the two values together to get the increase in the current.

Let us calculate the current,

Rearranging the above equation, we will get

$\frac{{\mathrm{I}}_{\mathrm{final}}}{{\mathrm{I}}_{\mathrm{initial}}}=\frac{{\mathrm{B}}_{\mathrm{Initial}}}{{\mathrm{B}}_{\mathrm{Final}}}\phantom{\rule{0ex}{0ex}}=\frac{100}{95}\phantom{\rule{0ex}{0ex}}=1.053$

Rearranging the above equation, we will get

${\mathrm{I}}_{\mathrm{Final}}=1.053{\mathrm{I}}_{\mathrm{Initial}}\phantom{\rule{0ex}{0ex}}={\mathrm{I}}_{\mathrm{Initial}}+0.053{\mathrm{I}}_{\mathrm{Initial}}\phantom{\rule{0ex}{0ex}}={\mathrm{I}}_{\mathrm{Initial}}+5.3%{\mathrm{I}}_{\mathrm{Initial}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

Hence, the required percent of the increase in the current is 5.3%.