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

A distant telephone, whose resistance is 300 ohms, is connected to the exchange 10km away by a pair of wires whose resistance singly is 50 ohms/km. A twig falls across the wires at a certain point producing the effect of a resistance, R, between the wires at that point. Measurements made at the exchange show a resistance between the ends of the wires of 130 ohms which rises to 160 ohms when the distant telephone is disconnected.

How far from the exchange is the twig to be found and what is the value of R?

2. Relevant equations

As far as I can tell, all that is needed is..

SERIES

∑R = R1 + R2 + R3 etc..

PARALLEL

1/∑R = 1/R1 + 1/R2 + 1/R3 etc..

3. The attempt at a solution

I tried to get two simultaneous equations in R and x (with x being the distance of the twig to the exchange)

So for my first equation, I said.. ∑R=R+(5x*2)

so.. 160=R+10x

For my second equation, I said.. 1/∑R = 1/(R+10x) + 1/(300+2*5*(10-x))

so.. 1/130 = 1/(R+10x) + 1/(400-10x)

However solving these simultaneous equations is proving brutal - I can't get the second one in a nice form. Any help?

Thanks!

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