Question

A metal wire has a resistance of 60 ohm it is cut into 3 equal lengths find the equivalent resistance when two parts are connected in a parallel and third part is with series
.

Answer 1

Answer:

Explanation:

p=RA/L (resistivity = resistance x cross-sectional area/length) rearranges to give: R=pL/A

Now looking at the equation, you can see that if the length of the wire decreases 3x, the resistance in the wire also decreases 3x. So the resistance of one of the new smaller wires (made by cutting the initial wire) will be 60/3=20Ω

if two are in series, then the total resistance in that part is 20+20=40Ω (lets call this R1), however when there is a third wire in parallel (R2) the combined resistance is:

1/Rtotal=1/R1+1R2 so 1/Rtotal=1/40+1/20=3/40

the reciprocal of 1/Rtotal is 1/(3/40)=40/3Ω