Question

If a resistor having resistance 'R' is cut into three equal parts, then the equivalent of parallel combination is?​

Answer 1

Since,

Resistance $\propto$ Length

Consider the relation,

$\boxed{ \boxed{ \sf\dfrac{R_1}{R_2} = \bigg( \dfrac{l_1}{l_2} \bigg) {}^{2} }}$

When resistor is cut into three pieces, length is reduced by 3 times.

Therefore,

$\sf\dfrac{R}{R'} = \bigg(\dfrac{ l }{ \frac{l}{3} } \bigg) {}^{2} \\ \\ \implies \sf \: R' = \dfrac{R}{9}$

Also, for resistance - cross sectional area cases :

Resistance $\propto$ 1/(Radius)²

Consider this,

$\boxed{ \boxed{ \sf\dfrac{R_1}{R_2} = \bigg( \dfrac{r_2}{r_1} \bigg) {}^{4} }}$