Question 4: Why does the back emf tend to decrease as the rate of doing work increases?
Here I = current provided to the coil
V = voltage provided to the coil
R = resistance of the coil
ε = back emf
Multiply throughout by R, equation (i) becomes
Multiply this equation by I,
If we analyze the above equation, we find that I2R is the power dissipated (i-e, used) in the coil, IV is the input power by the electric energy source and Iε is the power used to do work against the back emf.
Rearrange equation (ii)
So the power supplied by the source (IV) is equal to the sum of the power dissipated in the coil and the power used to do work against the back emf.
We see that when the rate of doing work (= power = I2R) increases, the factor Iε decreases. Current is the common multiplier, therefore, the back emf ε will decrease.
Note that the decrease in the back emf allows the motor to draw more current.