What is new voltage?

Question

Electic motor plugged into electric socket with frequency 60 Hz and ajustable voltage.
Initially voltage is set at Uo = 100V.

The motor draws current Io = 1A,
and consumes power Po = 60W.

During the operation resistance of wire
in motor coils increased by ∆R = 90 Ohm
due to overheating.

To what new value U1 should the voltage
be adjusted, if we want the motor to operate
under the same load wth the same RPM?

Answer 1

First calculate the initial resistance in the motor from power = I^2xR. R = 60/1^2 or R = 60 ohms.

Then calculate the initial impedance (resistance and inductance) from V=IxZ; Z=100/1; Z = 100 ohms.

Consider Z as the hypotenuse of a right triangle with the sides being R and X. X is the reactance of the inductive part of the load. For that triangle, Z^2 = R^2 + X^2 and X = sqrt(Z^2 -R^2); X = 80 ohms.

When ∆R = 90 ohms is added, the new R is 150 ohms. New Z is sqrt(150^2 + 80^2); Z = 170.

To keep the current the same, the voltage needs to b increased to 1A x 170 ohms = 170 volts. If the current is the same, the torque should be the same. If the motor is an induction motor, the speed is mostly determined by the frequency which hasn’t changed. If it is a universal motor, we will assume that the back emf is the same because the current through the inductive part of the load is the same and X hasn’t changed.

Answer 2

I went and asked Chas EE to answer this question for you. He was the first person who came to mind when I saw it again.

Oh, and thanks Chas.