(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use Kirchhoff’s junction rule and loop rule (twice) to find the effective resistance of the two

resistors connected in parallel as shown, and demonstrate that this agrees with the expression1/R = 1/R_{1}+ 1/R_{2}

(poorly drawn picture of the circuit)

3. The attempt at a solution

Using Kirchoff's 1st law:

I_{1}= I_{2}+ I_{3}

Using Kirchoff's 2nd law:

E - I........ [1]_{2}R_{1}= 0

and

I........ [2]_{2}R_{1}- I_{3}R_{2}= 0

Now I think I can say thatE = ISubtituting that into equation [1] gives:_{1}R

I_{1}R - I_{2}R_{1}= 0

Now here's where I'm having difficulty, I keep trying out different ways of substituting the equations into one another but end up with stupid answers like R = R_{2}...

Could anyone point me in the right direction?

Thanks in advance

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# Homework Help: Kirchoff's rules & resistors in parallel

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