Question

A alluminium wire having resistance R is cut into four equal parts (1)Find the resistance of each part in terms of original resistance of the wire and (2)Find the resistance of the combination of there four parts are connected in parallel?​

Answer 1

(1) resistance of each part is R/4

(2)

$\frac{1}{ r _{p}} = \frac{1}{r1} + \frac{1}{r2} + \frac{1}{r3} + \frac{1}{r4}$

as we know

r1 = r2 = r3 = r4 = r = R/4

then

$\frac{1}{ r _{p} }= \frac{4}{r}$

$r _{p} = \frac{r}{4}$

or

putting r = R/4

$r _{p} = \frac{R}{16} ohm$