Maximum Potential Difference in Parallel Resistors with Equal Resistance

[lha08]

Homework Statement

Given three 4 ohms resistors rated at 20 W, find the maximum potential difference that can be applied if they are connected all in parallel...

Homework Equations

The Attempt at a Solution

so in this case i first calculated the current using P= I^2R, which gives I=2.24 A. Like at first, i used V=IR and just plugged in the values for the current I just found and 4 ohms for the resistor, and i got the right answer, which is 8.94 V...but then i started double guessing myself, like i was wondering why exactly did we not divide the current by 3 seeing as though the resistors are in parallel with the same resistance values?...Does it have something to do with the fact that they are asking for the maximum potential difference?

 

[collinsmark]

so in this case i first calculated the current using P= I^2R, which gives I=2.24 A. Like at first, i used V=IR and just plugged in the values for the current I just found and 4 ohms for the resistor, and i got the right answer, which is 8.94 V

Looks good to me. (You could have just used P = V²/R, but the way you did it works too.)

...but then i started double guessing myself, like i was wondering why exactly did we not divide the current by 3 seeing as though the resistors are in parallel with the same resistance values?...Does it have something to do with the fact that they are asking for the maximum potential difference?

The 4 Ω value and 20 W rating are specific to the specific resistor (whether or not you are using multiple numbers of them in a circuit). So when you deal with these numbers, they are only applicable to a single, physical resistor. So, when dealing with these numbers, you must treat the resistor individually.

So why did the problem statement even bother to mention that there were 3 resistors in the circuit? I mean, even if there were 100 resistors it wouldn't have changed the maximum potential, right? I'm guessing the answer has to do with something later in the problem. Such as a comparison to what the answer would be if you connected them in series (instead of in parallel). Then compare the max source current and maximum potential (at the source) in both situations.

 

[lha08]

Looks good to me. (You could have just used P = V²/R, but the way you did it works too.)
The 4 Ω value and 20 W rating are specific to the specific resistor (whether or not you are using multiple numbers of them in a circuit). So when you deal with these numbers, they are only applicable to a single, physical resistor. So, when dealing with these numbers, you must treat the resistor individually.

So why did the problem statement even bother to mention that there were 3 resistors in the circuit? I mean, even if there were 100 resistors it wouldn't have changed the maximum potential, right? I'm guessing the answer has to do with something later in the problem. Such as a comparison to what the answer would be if you connected them in series (instead of in parallel). Then compare the max source current and maximum potential (at the source) in both situations.

Thanks a lot! I'm just wondering, like I'm thinking that because the potential difference is the same through resistors that are in parallel, then if we look at the values of the resistors, like they're asking for the MAX value of potential difference , then in parallel, one resistor of 4 ohms would give the highest value for potential difference compared to when we take the equivalent resistance of all 3 resistors, which would give a lower value? Does that make sense or am i overthinking thinking it?

 

[collinsmark]

Thanks a lot! I'm just wondering, like I'm thinking that because the potential difference is the same through resistors that are in parallel, then if we look at the values of the resistors, like they're asking for the MAX value of potential difference , then in parallel, one resistor of 4 ohms would give the highest value for potential difference compared to when we take the equivalent resistance of all 3 resistors, which would give a lower value? Does that make sense or am i overthinking thinking it?

No, you're not over-thinking it at all! It all makes sense when you do the calculations for power.

There are 3 resistors, and each is dissipating 20 W. So all three resistors together are dissipating a total of 3 x 20 W = 60 W.

Now find the equivalent resistance of the 3 resistors in parallel. Use the equivalent resistance and the known 8.94 V voltage to find the current coming from the source, using I = V/R_eq (alternately, you could just add up the current going through each individual resistor -- but try it this time by finding the equivalent resistance, just to demonstrate the issue). Now find the power coming from the source (P = VI, where I is the current coming from the source). If you did the math right, you should find that conservation of energy actually works.