Power dissipated by a resistor

In summary, the conversation discusses the concept of power dissipated by a resistor and how it relates to voltage. The conversation also mentions different formulas that can be used to calculate power, and how doubling the voltage can result in a fourfold increase in power. The conversation ends with the confirmation of the answer to the original problem, which stated that a 10 ohm resistor dissipates 1 watt of power when connected to a DC voltage source, and if the value of the DC voltage is doubled, the resistor will dissipate 4 watts of power.
  • #1
salomi
6
0
hi just needed to know if the power dissipated by a resistor is equal to the total voltage. I am having a hard time understanding a problem i was given, and i know the formulas to find power dissipated, but i can't use P = I squared * R or P = V squared / R for this question...

" A 10 ohm resistor dissipates 1 W of power when connected to a dc voltage source. If the value of dc voltage is doubled, the resistor will dissipate?"

My teacher said the answer is 4 watts, but he never actually worked it out for me, and i would like to know how he got that answer, rather than just believe him. How do i find the power dissipated if I'm not given the voltage? Is the 1W of power dissipated by the 10 ohm resistor equal to my total Voltage? As you can see this problem is driving me crazy, and I've been stuck and not sure how to figure it out. Someone PLEASE help me out! It is probably not as hard as i am making it, but thanks in advance.
 
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  • #2
salomi said:
hi just needed to know if the power dissipated by a resistor is equal to the voltage.
Power and voltage are two different things with different units. They cannot be equal.
i know the formulas to find power dissipated, but i can't use P = I squared * R or P = V squared / R for this question...
Why can't you?
How do i find the power dissipated if I'm not given the voltage?
If you wanted to calculate the voltage across the resistor, you could. But there's no need.

Hint: The second formula for power is all you need.
 
  • #3
You can use these equations for this question.
You know that power P = I^2 x R
also power P = V^2/R

In each of these cases if you double I power will be 4x greater (if R does not change)
Also if you double V power will be 4x greater (if R does not change)
 
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  • #4
Thank you so much for the quick responses. Although the answer is probably right in front of my face, i am still getting confused by the fact that my power dissipated is in watts. If i plug in the numbers, my equation reads " 1W^2 divided by 10 ohms which gives me 0.1 Volts? But the question is asking for power dissipated by the resistor if voltage is doubled and resistance stays the same. Am i plugging in the numbers wrong?
 
  • #5
Try this: Don't plug in any numbers. Looking at the power formula, just state what happens to the power if the voltage doubles.
 
  • #6
I think this is where i am most confused. What is my Voltage for the problem? It can't be the power dissipated, right?
Trying it your way, if i double the V, my power will also double? I feel like I am not given enough information and i would have to calculate my current in order to get the answer. But before i can do that, i would have to know my total voltage. I'm sorry if i am giving too many questions at one time, i just don't understand power dissipation that well i guess lol
 
  • #7
Don't forget that Power = V x I and for a resistor if you double V then I will also double.
So making V 2x greater, makes I also 2x greater which means power mis 4x greater.
However you do it
P = VxI
P = V^2/R
P = I^2R
These are all versions of the same equation
 
  • #8
salomi said:
I think this is where i am most confused. What is my Voltage for the problem?
You don't need to know the voltage, only that it doubles.
It can't be the power dissipated, right?
No, that makes no sense.
Trying it your way, if i double the V, my power will also double?
Nope. That would be true if power were proportional to the voltage, but it's proportional to the voltage squared.

P = V2/R. What happens if you replace V with 2V?
 
  • #9
Again thank you very much for all your help. I finally understand what you both are telling me. If the voltage across a resistor is doubled, the power dissipation in the resistance increases by a factor of 4.
But when i use 2V^2 i get 4V. So now i divide by resistance? Given the information you both have provided, i try and work the problem, my answer is a decimal.
I tried this - 1w = V^2 / 10 ohms. I'm sure this is wrong since my answer isn't anywhere near 4 watts. What am i doing wrong?
 
  • #10
salomi said:
If the voltage across a resistor is doubled, the power dissipation in the resistance increases by a factor of 4.
Good. That's all you need to know to solve this problem.

What's the original power? When you double the voltage, you multiply that power by 4. So what's the new power?
 
  • #11
my original power was 1W. my new power is 4W since my voltage was doubled. I really appreciate Doc Al and technician for the past hour! Great forum you guys!
 
  • #12
If you look at your original statement. a 10ohm resistor dissipated 1Watt then this tells you that the original voltage must have been
V^2/R = 1Watt so V^2 = 1 x R = 1 x 10 so V =√10 = 3.16V
If this voltage is doubled to 6.32V then power = V^2/R = 6.32^2/10 = 4 watts
See... your numbers confirm it
 
  • #13
Can't thank you both enough! Simple problem but man was it giving me a heck of a time :) Have a great new year fellas!
 

What is power dissipation?

Power dissipation is the process by which energy is transformed and released as heat through a resistor. It is measured in watts (W) and is the product of the voltage across the resistor and the current flowing through it.

How is power dissipation calculated?

The power dissipated by 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, if the resistance (R) of the resistor is known, the formula P = I^2R can also be used.

Why is power dissipation important?

Power dissipation is important because it can affect the performance and safety of electronic circuits. Excessive power dissipation can lead to overheating, which can damage components and reduce the lifespan of the circuit. It is also important to consider power dissipation when designing circuits to ensure that the components can handle the amount of heat generated.

How does the resistance of a resistor affect power dissipation?

The resistance of a resistor directly affects the power dissipation. A higher resistance will result in a higher power dissipation, given the same voltage and current. This means that resistors with higher resistance values can dissipate more power and may need to be chosen for high-power applications.

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

There are several ways to reduce power dissipation in a circuit. One way is to use a resistor with a higher power rating, as it will be able to handle more heat. Another way is to use multiple resistors in parallel, which will distribute the power dissipation among them. Additionally, using a lower voltage or decreasing the current can also reduce power dissipation. Finally, incorporating heat sinks or fans can help dissipate excess heat from the circuit.

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