Power dissipated by a resistor in a circuit

In summary, the conversation is about finding the power in a circuit using the formula P = V^2 / R, and the attempt at a solution involves collapsing parallel resistors and using Kirchhoff's voltage law. The final answer is determined to be option D, but the answer key lists option B as the correct answer.
  • #1
plazprestige
33
0

Homework Statement



Screen Shot 2015-02-05 at 11.23.06 AM.png


Homework Equations



P = V^2 / R
1/Rt = sum(1/Ri) (parallel)

The Attempt at a Solution


[/B]
Since all the answer choices express the solution in terms of V^2 / R, I tried to find the voltage drop across resistor #2 to find the power. I collapsed the two parallel resistors 2 and 3 into one and found their effective resistance to be R/2 (parallel formula). Using Kirchhoff's voltage law,

V = IR + I(R/2) = 3IR / 2 where I is the total current in the circuit

Since V = 3IR/2, I can rewrite the voltage drop across the collapsed resistors as (⅓)V. Therefore the voltage drops across resistors #2 and #3 are both (⅓)V since they are in parallel. Plugging into the power formula,

P = (1/3V)^2 / R = V^2 / 9R, answer choice D. But the answer key says the solution is B. Why?
 
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  • #2
Your reasoning looks correct to me. I agree that D is the correct answer. Apparently the answer key is wrong.
 
  • #3
I agree.
 

1. What is power dissipation in a resistor?

In simple terms, power dissipation in a resistor is the amount of energy that is converted into heat when an electric current passes through it. This heat is a result of the resistance of the resistor, which causes a voltage drop and generates heat.

2. How is power dissipation calculated in a circuit?

The power dissipation in a resistor can be calculated using the formula P = VI, where P is power in watts, V is voltage in volts, and I is current in amperes. Alternatively, it can also be calculated using the formula P = I²R, where R is the resistance of the resistor in ohms.

3. Why is power dissipation important to consider in a circuit?

Power dissipation is important because it determines the maximum amount of current that can flow through a resistor without causing it to overheat. This can help prevent damage to the resistor and ensure the circuit functions properly.

4. How does the power dissipation affect the choice of resistor in a circuit?

The power dissipation rating of a resistor is an important factor to consider when choosing a resistor for a circuit. A resistor with a higher power dissipation rating can handle more current without overheating, making it suitable for use in high-power circuits.

5. What are some ways to reduce power dissipation in a circuit?

One way to reduce power dissipation in a circuit is by using resistors with a higher power rating. Another way is to use multiple resistors in parallel instead of one single resistor, as this can distribute the power dissipation among them. Additionally, choosing a lower voltage power supply can also help reduce power dissipation in a circuit.

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