Question

A piece of wire having a resistance R is cut into five equal parts. 

(a) How will the resistance of each part of the wire change compared with the original resistance? 

(b) If the five parts of the wire are placed in parallel, how will the resistance of the combination change? 

(c) What will be ratio of the effective resistance in series connection to that of the parallel connection?

Answer 1

(a) Original resistance

R = \(\frac{l}{A}\)

∴ R α l

After cutting length of each piece

r = \(\frac{l}{5}\)

New resistance

R' = \(\frac{l'}{A}\)

R’ α l’

\(\frac{R}{R'} = \frac{l}{\frac{l'}{5}}\) = 5

R : R' = 5 : 1

(b) When five parts of the wire are placed in parallel. 

Effective Resistance

Resistance of the combinations

R_P = \(\frac{R}{25}\)

(c) When resistance are connected in series

R_S = R

When resistance are connected in parallel

 R_P = \(\frac{R}{25}\)

R_S : R_P = R : \(\frac{R}{25}\)

= 25 R : R₁

R_S : R_P = 25 :1