Potential Difference and Power in Resistor Circuit

In summary, the conversation is about a practice exam problem that involves using equations to solve for current and power in a circuit. The student is confused about the answer provided by their professor and asks for clarification. The expert explains the correct answer and points out a potential mistake in the student's calculations. The conversation also touches on the concept of potential difference and how it relates to voltage in a circuit.
  • #1
Gwozdzilla
81
0

Homework Statement


I attached a screenshot of the problem(s) that my professor gave in a practice exam.

Homework Equations


∑I = 0 at each junction
∑V = 0 at each closed loop
P = I2R = V2/R
Rseries = R1 + R2 +...

The Attempt at a Solution


Part A:
I think the current I in the center, broken line of current, is zero because that wire is broken. Then
I1+I2 = 0. So I1 = I2 = I

Going around the large loop, starting from the battery at the top:

V + V - IR - IR = 0
2V = 2IR
V=IR
12 = I(10)
I = 1.2

In the bottom loop...

Va + V - IR + V = Vb
Va - Vb = -2V + IR
Va - Vb = -2(12) + (1.2)(10)
Va - Vb = 12V in absolute value...
Is absolute value what I'm looking for? +12V is the answer in the solutions my professor provided.

Part B:
Rseries = R1 + R2 +...
Rseries = 10 + 10
Rseries = 20

P = I2R = V2/R
P = (1.2)2(20) = 28.8W
P = (12)2/(20) = 7.2W

These aren't equal. I tried it with R in parallel as well (Req = 5), and it's still wrong. In the answers provided each of the power equations are multiplied by 2 and R = 10. Why is all of this?

Thanks!
 

Attachments

  • 2006 Final.13.jpg
    2006 Final.13.jpg
    11.5 KB · Views: 411
Physics news on Phys.org
  • #2
Gwozdzilla said:

Homework Statement


I attached a screenshot of the problem(s) that my professor gave in a practice exam.

Homework Equations


∑I = 0 at each junction
∑V = 0 at each closed loop
P = I2R = V2/R
Rseries = R1 + R2 +...

The Attempt at a Solution


Part A:
I think the current I in the center, broken line of current, is zero because that wire is broken. Then
I1+I2 = 0. So I1 = I2 = I

Going around the large loop, starting from the battery at the top:

V + V - IR - IR = 0
2V = 2IR
V=IR
12 = I(10)
I = 1.2

In the bottom loop...

Va + V - IR + V = Vb
Va - Vb = -2V + IR
Va - Vb = -2(12) + (1.2)(10)
Va - Vb = 12V in absolute value...
Is absolute value what I'm looking for? +12V is the answer in the solutions my professor provided.

Va-Vb=-12 V, The potential increases from a to b by 12 V. Look at your notes, what Uab means, it might be Vb-Va.

Gwozdzilla said:
Part B:
Rseries = R1 + R2 +...
Rseries = 10 + 10
Rseries = 20

P = I2R = V2/R
P = (1.2)2(20) = 28.8W
P = (12)2/(20) = 7.2W

The 28.8 V is correct. The voltage is 24 V across the two series resistors, so P=242/20, the same as before.

ehild
 

FAQ: Potential Difference and Power in Resistor Circuit

1. What is potential difference?

Potential difference, also known as voltage, is the difference in electric potential energy between two points in an electric circuit. It is measured in volts and is represented by the symbol V.

2. How is potential difference related to current?

According to Ohm's Law, potential difference is directly proportional to current, meaning that as the potential difference increases, the current also increases. This relationship is represented by the equation V = IR, where V is the potential difference, I is the current, and R is the resistance of the circuit.

3. What is the difference between potential difference and power?

Potential difference and power are two different concepts in electricity. Potential difference refers to the difference in electric potential energy, while power refers to the rate at which energy is transferred or used. Power is measured in watts and is represented by the symbol P.

4. How is potential difference calculated in a resistor circuit?

In a resistor circuit, potential difference is calculated using Ohm's Law. The potential difference is equal to the current (I) multiplied by the resistance (R). This can be represented by the equation V = IR. For example, if a circuit has a current of 2 amps and a resistance of 5 ohms, the potential difference would be 10 volts.

5. How does potential difference affect the power in a resistor circuit?

According to the power formula, P = IV, potential difference plays a crucial role in determining the power in a resistor circuit. As the potential difference increases, the power also increases, assuming the resistance stays constant. This is because a higher potential difference allows for a greater flow of current, resulting in more energy being transferred per unit time.

Back
Top