Question

a piece of wire having a resistance R is cut into four equal parts . 1) how will the resistance of each part of the wire compare with the original resistance? 2) if the five parts of the wire are placed in parallel, how will the resistance of the combination compare with the resistance of the original wire? what will be ratio of resistance in series to that of parallel?

Answer 1

*Answer*:

*I hope it is correct*

*Explanation*:

(a) Resistance of a piece of wire is proportional to its length i.e. R∝l

Each piece has a resistance =R

Wire is cut into five equal parts

∴ Resistance of each part =R5

Resistance = R5

b) All the five parts are connected in parallel.

For parallel connection , the effective resistance is

1Rp=1R1+1R2

1RP=5R+5R+5R+5RRR

1RP=25R⇒∴RP=R25

The ratio of the effective resistance in series to paralle connection.

1RP=25Rs⇒RsRP=251

Ratio of R1&RP=25:1