Question

A wire of resistance 9 ohm having length 30 cm is tripled on itself. What is its new resistance?

Answer 1

Resistance (R) = 9 ohm

Length l = 30 cm

New Length (l) = 30 cm = `l/3` = 10 cm   

New area a_n = 3a

`R = ρ 1/a` 

Initial resistance `9 = ρ 30/a`  ...(i)

New resistance `R_n = ρ 10/(3a)`  ...(ii)

On dividing eqn (ii) by (i), we get,

`R_n/9 = (ρ 10/(3a))/(ρ 30/a)` 

`R_n /9 = 10/90` 

`R_n /9 = 1/9`

`R_n /1 = 9/9` 

R_n = 1 Ω

Hence, The new resistance = 1 ohm.