Question

A motor winding has a resistance of 80 ohm at room temperature of 20 deg C before switching on to a 230V supply. After 4 hours run the winding resistance is 100 ohm. Find the temperature rise if the material resistance temperature co-effiecent is 1/234.5 deg C.

Answer 1

Q171582

A motor winding has a resistance of 80 ohms at room temperature of 20 deg C before switching on to a 230V supply. After 4 hours run the winding resistance is 100 ohm. Find the temperature rise if the material resistance temperature co-efficient is 1/234.5 deg C.

Solution:

We are given the resistance of the material at 20 ^oC.

We will take this as our reference resistance and temperature.

R _ref = 80 ohms. T _ref = 20 ⁰C.

The effect of temperature on resistance is given by the relation

$R = R_{ ref} [ 1 + α ( T - T _{ref} ) ]$

where R _ref is the reference resistance, T_ref is the temperature at the R _ref.

α is the material resistance temperature coefficient.

R is the resistance of the material at temperature T.

We have,

R _ref = 80 ohms, T _ref = 20 ⁰C.

α = 1/ 234.5 ⁰C.

We have to find the temperature of the material when the resistance observed is 100 ohms.

So R = 100 ohms.

Substitute all this information in the formula we have

$100 ohms = 80 ohms [ 1 + \frac{1}{234.5^0C } ( T - 20 ^0C) ]$

divide both the side by 80 ohms we have

$\frac{100Ω }{80Ω } = [ 1 + \frac{1}{234.5^0C } ( T - 20 ^0C) ]$

$1.25 = 1 + \frac{1}{234.5^0C } ( T - 20 ^0C )$

subtract 1 from both the side we have

$1.25 -1 = 1 + \frac{1}{234.5^0C } ( T - 20 ^0C ) - 1$

$0.25 = \frac{1}{234.5^0C } ( T - 20 ^0C )$

multiply both the side by 234.5 ⁰C, we have

$0.25 * 234.5 ^0C = \frac{1}{234.5^0C } ( T - 20 ^0C ) * 234.5 ^0C$

$0.25 * 234.5 ^0C = T - 20 ^0C$

$58.625 ^0C = T - 20 ^0C$

add 20 ⁰C on both the side we have

T = 58.63 ⁰C + 20 ⁰C = 78.625 ⁰C.

which in 2 significant figure is 79 ⁰C.

Hence the final temperature of the motor winding will be 79 ⁰C.

in question, we are asked the temperature rise.

Temperature rise = Final temperature - initial temperature

= 79 ⁰C - 20 ⁰C

= 59 ⁰C.

Hence the temperature rise of the motor winding is 59 ⁰C.