Max Voltage for Series/Parallel Resistors of 5 Ohms/10 Watts

[mopar969]

The problem is:
Three 5 ohm resistors are each rated at 10 watts. What is the max voltage that can be applied if they are connected in
a: series
b: parallel

I know the properties for adding up resistors in parallel and series but how do you incorporate the 10 watts for each of the resistors to find the max voltage?

 

[gneill]

Determine either the voltage across or the current through each resistor as a function of the supply voltage. The power dissipated by each individual resistor is determined by its resistance and the voltage (or current). Do you know the various expressions for power dissipated in a resistance?

 

[mopar969]

I know that the total Resistance when the resistors are in series is 15 ohms and when they are in parallel is 5/3 ohms. However, I am not given any information about the powers supply so how do I finish the problem form here?

 

[gneill]

I know that the total Resistance when the resistors are in series is 15 ohms and when they are in parallel is 5/3 ohms. However, I am not given any information about the powers supply so how do I finish the problem form here?

You are to find the maximum value for the power supply voltage that will not destroy the resistors! So find the power dissipated in a resistor versus the power supply voltage, then find the voltage that just makes the power the maximum allowed (10W).

 

[mopar969]

How do you calculate the maximum voltage without knowing the current?

 

[gneill]

How do you calculate the maximum voltage without knowing the current?

The current depends upon the voltage applied. So you can find the current as a function of the voltage: I(V) = something.

What are the equations for the power dissipated by a resistor?

 

[mopar969]

I know that power in watts (like a generator rating) is volts times amps ( so p=vI) but how does this apply to a resistor?

 

[gneill]

Resistors get hot when they dissipate power. The power dissipated is the current through them multiplied by the voltage dropped across them: volts x amps. Think of it as the electrical equivalent of work done by friction.

But there are several other useful expressions for the power dissipated by a resistor where you only need to know the voltage or the current (since one can always be determined from the other via Ohm's law: R = V/I.

So, for example, If P = I*V, then also P = I²*R = V²/R

 

[mopar969]

For the resistors in series I got a max voltage of 12.25 volts and in parallel a max voltage of 4.08 volts are these correct?

 

[gneill]

They don't look correct to me. Show your calculations. Let's start with the parallel case.

 

[mopar969]

From p=vsquared divided by r v = square root of p times r. So for the series p is ten and r is 15. For the parallel p is ten and r is 5/3ohms.

 

[gneill]

Okay, I see where you've gone astray.

For the series case, each resistor has voltage V/3 across it. For the parallel case, each resistor has V across it.

You don't need to determine the net resistance for either case, just the voltage across each resistor (or, if you're so inclined, the current through anyone resistor in which case you may need the total resistance for the series version).

 

[mopar969]

Why is that? I know that the current is the same for them in a series etc.. But how did you determine that for the voltage? Once again thanks for all the help.

 

[gneill]

In a parallel connection, all components share the same voltage. In a series connection of identical resistances, the voltage drops distribute evenly across all of them.

 

[mopar969]

So then they have the same voltage of 1.08 volts?

 

[gneill]

So then they have the same voltage of 1.08 volts?

I don't know what you're referring to. But 1.08 V across 5 Ohms only produces 0.233W of power.

 

[mopar969]

I am sorry I am to type that each has 4.08 volts.

 

[gneill]

At 4.08V across 5 Ohms, the power dissipated is 4.08²/5 = 3.33W.

You're looking for 10W dissipation on each resistor.

 

[mopar969]

Why do you have a five don't you need a 15 for them in a series and 5/3 for them in parallel.

 

[gneill]

Why do you have a five don't you need a 15 for them in a series and 5/3 for them in parallel.

No, you want to know the maximum power dissipated for an individual resistor. Each resistor has a power rating of 10W. You don't want to destroy the resistors, so it's the individual component dissipation that you need.

 

[mopar969]

I got for both the series and parallel circuit the max voltage for each resistor is 7.07 volts. Is this correct for both circuits?

 

[gneill]

Yes, that voltage will result in 10W dissipation in a 5 Ohm resistor. Now you just have to work out what supply voltage will result in that voltage on the resistors for each configuration.

 

[mopar969]

Since there are three resistors wouldn't it be 3 times the voltage 7.07 for both parallel ans series?

 

[gneill]

Series, yes. Parallel, no. How is voltage divided across series resistors? How about parallel?

 

[mopar969]

Thats what I don;t know and I don't know how to figure it out.

 

[gneill]

Thats what I don;t know and I don't know how to figure it out.

That's pretty basic stuff. You might want to consult your text about series and parallel circuits.

 

[mopar969]

Okay so for series the max volatge is 3*7.07. And for parrallel the voltage is just 7.07. Right?

 

[gneill]

Right.