Analyzing Electrical Circuits: True and False Statements

[bob123]

So I have the following homework question about electical circuits. There's three different circuits shown: Circuit A is just a battery hooked up to a single resistor. Circuit B is a battery hooked to two resistors in series. Circuit C is a battery hooked to two parallel resistors. All the circuits are closed and all the batteries and resitors are identical. There's a list of five statements and we have to say which are true and which are false.

1. The total power dissipated in circuit C is twice the total power dissipated in circuit B.
2. The current through a resistor is the same in circuits A and C.
3. The voltage across a single resistor in circuit C is twice the voltage across a single resistor in circuit B.
4. The power dissipated in circuit A is twice the power dissipated in circuit B.
5. The current through a resistor is the same in circuits A and B.

I worked through this problem assuming the voltage supplied was 10 V, and the resistance of each resistor was 2 ohms. This is what I got (correct me if I'm wrong anywhere, and I'm sure I am):

1. Total power dissipated in C is 100 W (10 V total * 10 A total), total power dissipated in B is 25 W (10 V total * 2.5 A total). So 1 is false. I'm not sure if I'm doing the total power dissipated for Circuit B right.

2. The current through circuit A is 10 V / 2 ohms = 5 A. In Circuit C, the current through each resistor is 10 V / 2 ohms = 5 A. True.

3. The voltage across a single resitor in C is 10 V (since voltage remains the same across a parallel circuit, right?). The voltage across a single resistor in B is 5 V (2.5 A * 2 ohms). True.

4. Power dissipated in A is 50 W (10 V * 5 A). Again, I'm not sure if I'm figuring this right, but the total power dissipated in B is 25 W (10 V total * 2.5 A total). True.

5. Current through the resistor in circuit A is 5 A (10 V / 2 ohms). Current through a resistor in circuit B is 2.5 A (10 V / 4 ohms). False.

I tried this answer and the computer said it was wrong. Am I doing something wrong, or is this just an error with the online assignment?

 

[jamesrc]

If you're comfortable with algebra, there's no reason to substitute values in for voltage and resistance. That said:

1. you are correct
2. correct again
3. correct again
4. correct again
5. correct again

So I think you've got them all right. So, either we both messed up or the program is wrong. Let us know if you need anything clarified.

 

[bob123]

I can't stand algebra, so I just used real numbers. I e-mailed the prof about it, unfortunately he's out of town til Tuesday. That's why I asked about it here. Thanks for double checking these.

 

[gameguru]

The only problem I see is number 5 which can be argued as true. The question as you have it stated is "The current through a resistor is the same in circuits A and B." The key part of the question is "through a resistor." This may mean that only one resistor in B (2 ohms) is used, not the equivalent resistance (2ohms + 2ohms). We find 10V/2ohms = 5 amps which equals the current in A.

Of course this is only speculation, but worth a try. Hope it helps.

 

[gameguru]

The only problem I see is number 5 which can be argued as true. The question as you have it stated is "The current through a resistor is the same in circuits A and B." The key part of the question is "through a resistor." This may mean that only one resistor in B (2 ohms) is used, not the equivalent resistance (2ohms + 2ohms). We find 10V/2ohms = 5 amps which equals the current in A.

Of course this is only speculation, but worth a try. Hope it helps.

 

[turin]

I got:

1. F
2. T
3. T
4. T
5. F