Question

A 500 m long wire has a resistance of 20 Ω. How much must be cut off to reduce its resistance to 12 Ω?

Answer 1

Given quantities:

$l = 500m \space\space\space R = 20\varOmega \space\space\space R_1 = 12\varOmega \space\space\space\space\space\space \Delta l -?$

$R = \rho\frac{l}{S} \space\space\space\space\space\space R_1 = \rho\frac{l_1}{S}$

$\large\frac{R}{R_1} = \frac{l}{l_1} \to l_1 = \frac{R_1}{R}l=\frac{12}{20}*500 =$ $300m$

$\Delta = l - l_! = 200m$

The 200m wire is cut to reduce the resistance to 12$\varOmega$

Answer: 200m