# Homework Help: Resistor circuit

1. Nov 28, 2016

### David112234

1. The problem statement, all variables and given/known data

A shunt-wound DC motor with the field coils and rotor connected in parallel (see the figure) (Figure 1) operates from a 140 V DC power line. The resistance of the field windings, Rf, is 248 Ω . The resistance of the rotor, Rr, is 4.40 Ω . When the motor is running, the rotor develops an emf E. The motor draws a current of 4.24 A from the line. Friction losses amount to 41.0 W .

A
Compute the field current If.
B
Compute the rotor current Ir.
C
Compute the emf E.
D
Compute the rate of development of thermal energy in the field windings.
Express your answer in watts.
E
Compute the rate Pth,rotor of development of thermal energy in the rotor.
Express your answer in watts.
F
Compute the power input to the motor Pin.
G
Compute the efficiency of the motor.
2. Relevant equations
I=v/R

3. The attempt at a solution

For Part A it I2=140/248 = .565

For part B since the points A,B, and C have the same potential and the motor has a resistance you can use ohms law again.
I3 = 140/4.40 = 31.81
but that is wrong, why?

Also I do not understand the EMF part, so when the motor becomes active it will develop its own EMF that will lower the batteries voltage. But wouldn't that then change the current trough the battery, and it would no longer be able to create that EMF?
So the motor is dependent on the current caused by the batteries voltage which is dependent on the motor? How does that work?

2. Nov 28, 2016

### Hesch

The rotor will develop a back-EMF = E.

Thus the voltage that drives the current I3 through Rr = 140V - E

The batteries voltage is not lowered, but constant.

3. Nov 29, 2016

### David112234

What does "back" EMF mean?
the Hint gives me "Think of the back emf from the rotor as reducing the voltage difference from the power supply across the rotor."
But wouldn't the voltage difference across the rotor reach the battery since wires are equipotential? Shouldn't the voltage for A,B, and C be the same?
Where on the diagram would the voltage be different, and wouldn't that still change the current trough the rotor?

4. Nov 29, 2016

### Staff: Mentor

The back-emf appears within the motor, distributed over the rotor coil. The rotor winding also has a resistance though, thanks to the resistivity of the wire that it's made of. A simplifying assumption is to model the resulting distributed system as a single EMF source in series with a single net resistance. So the potential difference between the power supply and the back-emf source is effectively absorbed by the winding resistance.

5. Nov 29, 2016

### David112234

I don't understand anything you wrote.
The potential across A,B, and C are are equal, is that correct?
If the battery than develops an EMF where on the diagram would it be?

6. Nov 29, 2016

### Staff: Mentor

The potentials at A, B and C (with respect to the bottom node) are all the same. A, B, and C are in fact all one node.

The battery has a constant EMF of Vdc. The battery doesn't develop the back-emf, the motor's rotor coil does. It's inside the blue circle. That's why the blue circle is labeled with the variables ε and Rr, the back-emf and the coil resistance.

7. Nov 29, 2016

### David112234

Ok, so current flows from high to lower potential, from top of the rotor to the bottom. EMF does the opposite, it pushes charges to a higher potential. So the motor would create a voltage at point A, since those wires have the same potential than the potential at A,B, and C would now be Vfrom battery - Vfrom motor. Do you see my logic? Is it correct?

8. Nov 29, 2016

### Staff: Mentor

No, you seem to think that the node ABC can change potential. It can't.

All three points A, B, and C are fixed at potential Vdc. There is no flexibility with this as the battery is considered to be ideal with a fixed potential difference and the wires are taken to be perfect conductors.

The difference between Vdc and the back-emf ε will be dropped across the rotor resistance.

9. Dec 2, 2016

### David112234

Sorry for the late post,
I think my problem stems from not understanding behavior of circuits with more than 1 battery
Lets ignore the middle resistor and use a series circuit for simplicity

So V1 will create a current clockwise, V2 will create a current counter clockwise, which way will the current flow trough the resistor, the battery with the higher Voltage will overpower the other one, is that correct?

So would you be able to just add the Voltages, if battery 1 is 10V and battery 2 is 3V wouldn't the voltage trough the resistor be
10V-7V = 3V ?

I cant imagine what happens physically. If the battery with larger voltage is pushing the current through the other battery opposite direction it would regularly flow what is the EMF doing? How are the charges moving, are they moving up and then back down or are they constantly moving up but with less energy because of the EMF?

10. Dec 2, 2016

### Staff: Mentor

Current flows though a component, voltage is measured across a component. Voltage does not flow through a component.

Potential changes in a circuit sum as you go around the circuit. This is the basis of Kirchhoff's Voltage Law (KVL) wherein if you sum all the potential changes around a closed path the sum will be zero. So in your example circuit, as you do a "KVL walk" clockwise around the circuit the potential differences for the two batteries will sum as +10V - 3V = 7 V. So the net EMF driving the circuit is 7 V, and this 7 V must be dropped across the resistor R if the total sum around the circuit is to be zero.

The current that enters a battery "in reverse" tends to recharge the battery. The EMF of a battery is typically generated through a chemical reaction that separates charges. When you force current through such a cell in reverse it tends to drive the chemistry the other way. Note that not all batteries are designed to make this process efficient or even workable depending upon how the chemistry sequesters the "spent" components in normal operation. This is why you can by "disposable" and "rechargeable" versions of batteries.

11. Dec 2, 2016

### David112234

I made an error there, the lower picture depicts what I meant to write,
So if battery 1 is 10V and battery 2 is 3V wouldn't the current through the resistor be as if there was just 1 (7)V battery instead?

And the recharging of the battery, lets assume they don't discharge and are perfect sources.
The charges are moving up with a U of q(10) but the EMF pointing down is trying to force them downwards and taking away some U of q(3) so the charges by the time reach the resistor they have q(7)J. Is that correct?

12. Dec 2, 2016

### Staff: Mentor

Yes.
Conceptually that is true, given that a potential difference has units of Joules per Coulomb.

13. Dec 12, 2016

### David112234

So now I have understood how a circuit behaves with two batteries, going back to the original problem, at point C why wouldnt you add the voltages from the battery and from the motor? When the motor is creating an EMF dont you have a circuit with two batteries?

14. Dec 12, 2016

### Staff: Mentor

The potential at point C is fixed by the battery voltage because there is no resistance between point C and the battery connection. All of the node ABC is fixed by the battery voltage. The emf of the motor is not directly connected between the common node and point C; there is the resistance of the rotor winding in the path. See the diagram in post #8 where the equivalent circuit for the emf and rotor resistance is indicated. The rotor current will create a potential drop across this resistance.

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