Question

A wire having uniform resistance 20 ohm cuts into 4 equal parts and are connected in parallel. Find the

net resistance of this combination.​

Answer 1

$\large \underline \bold{Given}$:-

A wire having uniform resistance 20 ohm cuts into 4 equal parts and all equal parts are connected in parallel .

$\large \underline \bold{To \: Find}$:-

Calculate the net resistance of this combination ?

$\large \underline \bold{Usable \: Formula}$:-

$\rm{parallel \: combination \: of \: R1 \: , \: R2 \: , \: R3 \: ,...., \: Rn.}$

$\rm{Equavalent \: Resistance \: -}$

$\rm{\dfrac{1}{R} \: = \: \dfrac{1}{R_1} \: + \: \dfrac{1}{R_2} \: + \: \dfrac{1}{R_3} \: + \: ..... \: + \: \dfrac{1}{R_n}}$

$\large \underline \bold{Solution}$:-

$\rm{Total \: resistance \: of \: a \: wire \: = \: 20}$Ω

when 20 Ω resistance is cut into 4 equal parts.

then ,

$\rm{the \: resistance \: of \: each \: part \: = \: 5}$Ω

$\rm{R_1 \: = \: R_2 \: = \: R_3 \: = \: R_4 \: = \: 5}$Ω

$\rm{all \: parts \: are \: connected \: in \: parallel \: combination.}$

$\rm{then \: ,}$

$\rm{The \: net \: resistance \: -}$

$\rm{\dfrac{1}{R} \: = \: \dfrac{1}{5} \: + \: \dfrac{1}{5} \: + \: \dfrac{1}{5} \: + \: \dfrac{1}{5}}$

$\rm{\dfrac{1}{R} \: = \: \dfrac{4}{5}}$

$\rm{R \: = \: \dfrac{5}{4}}$

$\rm{R \: = \: 1.25}$Ω

$\rm{Net \: resistance \: of \: this \: combination \: is \: 1.25 \: ohm.}$

Answer 2

Question

A wire having uniform resistance 20 ohm cuts into 4 equal parts and are connected in parallel. Find the net resistance of this combination