What is the maximum voltage across a 6 ohm, 1 watt resistor?

Can you apply that voltage safely to the 4 ohm resistor without the 4 ohm resistor blowing up?

 

edit: sorry!

Thank you for helping me!

 

I'm definitely piping in late in the game, but perhaps this (hopefully) more easily visualized example will help.

Imagine I have three 10ft ropes, one can support 100lb, one 200lb, and one 300lb before they break. I now tie them together end to end giving me a 30ft rope. How much weight can the combined rope support? Answer, just 100lb, because the configuration of the ropes forces the same tension on each and the limit is estalblished by the weakest of the ropes. Now imagine that instead I tie them in parallel such that each one is supporting the load equally (so they have the same load on them still). Now how much can be supported without any of them failing? 300lb, because each will be carrying 100lb just before the weakest one fails.

So you have to not only look at the combined capabilities, but also look at which individual component is going to set a limit, as it's capabilities are reached, that will/might prevent the other components from being able to operate at their respective limits.

 

@pulsed!Plz dont disclose the answer

 

destinyschild,

Pulsed was the OP in this thread. I had hoped he would show his work or indicate the answers to the ancillary questions asked of him to ensure he understood the original inquiry, but he choose not to.

We can only assume that they understood where they made the error ... till we have evidence that he didn't.

That is typical in the "homework" section.

 

Hello,

We have helped Pulsed (who started the thread) to have the correct answer.
Pulsed gave the correct answer in post #22, wich is 2.6666
The power in the 4 Ohms resistors is (2*2)/4 = 1 Watt.
The power in the 6 Ohms resistor is (2*2)/6 = 0.6666 Watt.
So the total power is 1 + 1 + 0.6666 = 2.6666 Watt.

Bertus

 

I think I made my error, with my answer of 3W, because 3 4ohm resistors in parallel would equal 3W.

So if I had, for example 4 resistors in parallel, say a 3R, 6R, 4.5R and 1.6R. Each with a wattage rating of 0.5W the maximum wattage across the composite resistor would be:

V = 0.5W * 0.742 = 0.371 Taking that to be the voltage...

Power total is: (0.176/3)+(0.176/6)+(0.176/4.5)+(0.176/1.6) or 0.2363W? Correct me if I am wrong.

 

Wrong. The lowest value resistor sets the maximum voltage from which each branch power is derived.

\(E=\sqrt{0.5\cdot1.6}\)

\(E=\sqrt{0.8}\)

\(E=0.894\)

Without simplification, the whole power formula would look like this:

\(P_T=\frac{\sqrt{(0.5W\cdot1.6 \Omega)}^2}{1.6 \Omega}+\frac{\sqrt{(0.5W\cdot1.6 \Omega)}^2}{3 \Omega}+\frac{\sqrt{(0.5W\cdot1.6 \Omega)}^2}{4.5 \Omega}+\frac{\sqrt{(0.5W\cdot1.6 \Omega)}^2}{6 \Omega}\)

Simplified, the formula becomes:

\(P_T=\frac{0.8}{1.6 \Omega}+\frac{0.8}{3 \Omega}+\frac{0.8}{4.5 \Omega}+\frac{0.8}{6 \Omega}\)

Solved:

\(P_T=0.5W+0.27W+0.18W+0.13W=1.08W\)

 

When you throw a number out, such as the 0.742, it would really be helpful if you showed where it came from. It would also help if you tracked your units. As it is, you have voltage equals power.

You know the answer has to be at least 0.5W total because the limit is set when the first resistor reaches 0.5W. You also know that the answer has to be no greater than 2W, which would be the case only if all of the resistors were the same resistance.

You know that the limit is set by the smallest resistor, since it will have the greatest current (and they all have the same voltage).

Q1) What resistor is the smallest?

Q2) What is the voltage across that resistor when it is dissipating power P (in terms of R and P)?

Q3) What is the power dissipated by each of the remaining three resistors (in terms of P, the R should drop out) when the smallest one is dissipating P?

Q4) What is the total max power dissipation of all four (in terms of P)?

Q5) What is the total max power dissipation for P=0.5W?

NOTE: You should get an answer between 1.25W and 1.50W.

If it was 1.5R instead of 1.6W, you could almost do it in your head.

 

0.742 is the composite resistance, which is where I went wrong.

Of course! You take the lowest valued resistance!

So we have: V = sqrt(P*R)

V = sqrt(0.5W*1.6R) = 0.89V

Total handling power of the composite resistor is therefore:

P = (V^2)*R

(0.8V/3R) + (0.8V/6R) + (0.8V/4.5R) + (0.8V/1.6R) = 1.2W

 

How do you come up with 0.89V I don't recall seeing a specific value for R (but I might have missed it). You don't need a specific value to get a specific answer to the problem.

You came up with 0.89V but then used 0.8V in your subsequent computations. That's one of the advantages of working symbolically and plugging in values only at the last part -- you are less likely to make those kinds of mistakes and more likely to catch them if you do.

 

0.894 is the calculated maximum voltage and 0.8 is 0.894 squared and rounded for use in the P=E/R power formula used for each resistor. The OP has some math errors and shows multiplication where he means division in one expression of the formula. I've edited post #28 above to show the steps.