# Homework Help: Resistance and Inductance

1. Oct 21, 2009

### songoku

1. The problem statement, all variables and given/known data
A motor has both resistance and inductance. A motor rated at 1 hp input operating at 240 V draws 4 A of current because

a. power is lost due to resistance
b magnetic saturation robs power
c. inductance does not consume power
d. friction in the bearings of the motor
e. (a) and (b)

2. Relevant equations
P = VI

3. The attempt at a solution
I try to calculate the current :

P = 1 hp $$\approx$$ 746 W

$$I = \frac{P}{V} = \frac{746}{240} = 3.1 A$$

In fact, the current drawn is bigger. I think maybe this has something to do with back e.m.f. but when back emf exists, the current drawn should be smaller (below 3.1 A). Can someone give me a hint to think about?

Thanks

2. Oct 21, 2009

### rl.bhat

In Ac circuit the average power consumption is given by
P = Vrms*Irms*cosφ. cosφ is called power factor. For pure resistance its value is one. For pure Inductance its value is zero. In LR circuit 0<cosφ<1.
Power is consumed to overcome losses due to friction,heating in the resistance etc.
In the circuit maximum current may be 4A, But because of power factor, it appears to be consuming only 3.1A.

3. Oct 21, 2009

### vk6kro

Motors are rated according to output power. So 1 HP is output.
So, 746 watts out but 960 watts into the motor.

Why would that be? What happened to the extra power?

4. Oct 21, 2009

Input power=output power(work done per second against back emf)+ resistance loss power(mainly joule heating losses).If the motor is loaded so that its speed reduces then,everything else being the same, the back emf will get smaller and the current will get bigger.

5. Oct 27, 2009

### songoku

Sorry for taking long time to reply.
Based on Mr. rl.bhat explanation, the extra power (difference between 764 W out and 960 W in) is consumed because of friction. Then the answer is (d).

I have another question. "P = Vrms*Irms*cosφ. For pure Inductance its value is zero."
This is related to choice (c). When it is pure inductance, then the average power consumed is zero. What is the meaning of this? Does this mean that inductance doesn't generate heat when current flows through it?
And what is the meaning of 'magnetic saturation" in choice (b)? I read a little about it from wiki but I don't get it....

Thanks

6. Oct 27, 2009

### rl.bhat

Based on Mr. rl.bhat explanation, the extra power (difference between 764 W out and 960 W in) is consumed because of friction. Then the answer is (d).
This is not entirely true. You can reduce the frictional loss to great extent by proper lubrication. Main loss is due to the heating of the resistance.
Current through pure inductance is called watt-less current, because it does not consume power.
In the motor, the coils were wound on the rotor and stator core made of steel. When AC current flows through them, they become magnetized and de-magnetized. When they are fully magnetized, it is called magnetic saturation. During magnetizing and demagnetizing some energy is lost in the core due to heating.

Last edited: Oct 27, 2009
7. Oct 27, 2009

### willem2

The question says the motor is rated at 1hp input. The output power of the motor is unknown. The question asks about the difference between the input power and the product of the input current and input voltage. Answers a, b, d and e are all not about input power but about output power, so they can't be right.

Back emf does reduce the input current, but it can reduce input power even more by making the input current more out of phase with input voltage.

8. Oct 27, 2009

### vk6kro

This is an obvious typo. Motors are rated in output power sometimes given in HP.
Horse power is a mechanical unit and motors produce mechanical output. They don't have mechanical input.

Last edited: Oct 27, 2009
9. Oct 31, 2009

### songoku

I don't know whether it's typo or not, but I have checked the question once again and it writes 'input'. And what's the meaning of "mechanical input"?

If during magnetizing and demagnetizing some energy is lost in the core due to heating, then it's true that "magnetic saturation robs power". Then, the answer will be (e). That's what I can come up with.

Thanks

10. Oct 31, 2009

### vk6kro

Something like a generator would have "mechanical input" because the shaft of the generator is rotated by power from another source. Possibly a gasoline engine or even a water wheel.

In that case, you could say the generator has a power input in Horse Power.

However a motor produces mechanical power from electrical power. It rotates the shaft and this can be used to make other things move.

This mechanical power output is the way that some motors are rated. It would be meaningless to say a motor had an input in Horse Power.

So, it is probably a typo and it would be worth querying it with whoever gave you the problem.