# Resistor in a Circuit with varying resistance.

1. Apr 22, 2013

### Jonnyto

1. The problem statement, all variables and given/known data
In the circuit of Fig. 23, ℰ, R1, and R2 have constant values but R can be varied. Find an expression for R that results in the maximum heating in that resistor.

2. Relevant equations
V=IR
resistors in parallel add up in inverse,
resistors in series add up directly,

3. The attempt at a solution
Okay so the way I undertook this problem was considering as R2 and R to be parallel, so I found the equivalent capacitance of those two. I got that new resistance and and then I considered R1 and then the new parallel system of parallels to be resistors in series. Later I used Kirchoff's Loop rule to isolate the new capacitance. ε-iReq=0
I used basic algebra to separate the R from all other values. Was this correct? I left the current, i, in the expression. The current is not actually part of the given.

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2. Apr 22, 2013

### Sunil Simha

You have obtained current through the required resistor as a function of R right? Plug that in the equation of the power dissipated by the resistor to obtain the power P as a function of R.

Now have you used calculus to find the minima or maxima of a function before?

3. Apr 22, 2013

### Jonnyto

Okay how would I solve it using power? Do I set up the power as a differential dw/dt?
However an issue is that i(the current is not isolated) and it is mixed within all the other values. I can only isolate either the varying resistance or the current or at least I think so.

4. Apr 22, 2013

### Staff: Mentor

Um, there' are no capacitors in the given circuit, so surely you're not finding equivalent capacitance. Equivalent resistance perhaps, but not capacitance.

Have you found an expression for the current through resistor R? If so, what did you find?

5. Apr 22, 2013

### Sunil Simha

Don't write P as dw/dt. Just write power as i2R. In this expression write i in terms of R. You don't need the actual value of i to solve this. (remember, i is the current through the unknown resistor.)

I just want to clarify whether they have taught you to use calculus to find the maxima and minima of a function.