MHB What is the Rate of Change of Resistance in a Parallel Circuit?

[musad]

Im having trouble with this problem to do with applictions of calculus.

If two resistors with resistances R1 and R2 are connected in parallel, then the total resistance R measured in ohms (Ω), is given by 1R=1R1+1R2.

If R1 and R2 are increasing at rates of 0.4Ω/s and 0.6Ω/s respectively, how fast is R changing when R1=10Ω and R2=90Ω?
Thanks

 

[chisigma]

Im having trouble with this problem to do with applictions of calculus.

If two resistors with resistances R1 and R2 are connected in parallel, then the total resistance R measured in ohms (Ω), is given by 1R=1R1+1R2.

If R1 and R2 are increasing at rates of 0.4Ω/s and 0.6Ω/s respectively, how fast is R changing when R1=10Ω and R2=90Ω?
Thanks

First consideration ... if R1 and R2 are connected in parallel, is $\displaystyle R = \frac{R_{1}\ R_{2}}{R_{1} + R_{2}} \ne R_{1} + R_{2}$, isn't it?...

Kind regards

$\chi$ $\sigma$

 

[MarkFL]

I suspect the OP meant to give:

$$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}\tag{1}$$

So, use (1) to determine $R$, and differentiate this with respect to time $t$, then plug in the given and computed values. What do you find?