Homework Help: Maximal duty cycle

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1. Apr 9, 2015

peripatein

1. The problem statement, all variables and given/known data
Assuming I have a 20V source on a “power resistor” which can withstand powers of up to 5 Watts on average before it excessively heats and damage begins. What is the DC current that runs through a resistor of 33ohm? What is its power dissipation? What is the maximal DC current I may run through it without damage, I5W? I am then asked to determine the maximal duty cycle allowed so the active load remains undamaged?

2. Relevant equations

3. The attempt at a solution
I found the DC current running through the resistor of 33ohm to be equal to 20/33=0.6A. The power equals I2R=11.9W. I5W=sqrt(5/33)=0.39A. Could the maximal duty cycle be found by simply dividing I5W by the first current, i.e. 0.39/0.6? If so, I am not quite sure why that is. Could someone kindly explain?

2. Apr 9, 2015

phinds

What would be the units of power/current? Do you think it could be a correct answer?

3. Apr 9, 2015

peripatein

It's 0.39A (not Watt!). I see no problem with the units, nor with dividing 0.39 by 0.6 in order to obtain a figure which has no units, such as duty cycle.

4. Apr 9, 2015

donpacino

P=I2*R

solve for I. Your resistor value is set (33 ohms). now you can find the current at any given power.....
edit: oops, you already knew that

per your question, think about what you are doing.
you are taking your max current assuming it is allways on, and dividing it by the max current your part can take.

Iavg=I*D

Pavg=Iavg2*R
we know Iavg=I*D
so
Pavg=(I*D)2*R

you know what I will be based on your earlier equations, solve for D.

Last edited: Apr 9, 2015
5. Apr 9, 2015

peripatein

Let's see whether I follow:
What's Iavg? Is it 20v/33ohm=0.6A?
And what's I? Is it I5W?

6. Apr 9, 2015

donpacino

sorry I was kind of scatterbrained there.

I is the current through the resistor with 20 volts across it.
Iavg is the average current through the resistor due to the duty cycle. so yes, by your notation Iavg=I5w

7. Apr 9, 2015

peripatein

Great, thank you!

8. Apr 9, 2015

phinds

You are making my point. Units of amps are NOT a dimensionless ratio, which is what a duty cycle is.

9. Apr 9, 2015

peripatein

What I carried out was Amp/Amp!

10. Apr 9, 2015

phinds

I was looking at your statement "dividing I5W by the first current" which is what I was alerting you to. Watts divided by amps is NOT dimensionless, it's volts.

11. Apr 9, 2015

peripatein

I5W is capital I (=current) and 5W as intended subscript, i.e. current for P=5W. Never mind.

12. Apr 9, 2015

phinds

Ah ha. Clearly I was not paying close enough attention. Sorry about that.