A piece of wire having resistance $R$ is cut into four equal parts. $(a)$ How will the resistance of each part compare with the original resistance ? $(b)$ If the four parts are placed in parallel, how will the joint resistance compare with the resistance of the original wire ?
A piece of wire having resistance $R$ is cut into four equal parts. $(a)$ How will the resistance of each part compare with the original resistance ? $(b)$ If the four parts are placed in parallel, how will the joint resistance compare with the resistance of the original wire ?
$(a)$ Since the wire is divided into four equal parts, therefore, the new length of each part becomes one-fourth of the original. Since resistance is directly proportional to length, hence, the resistance of each part becomes one-fourth of the original, $i . e ., RN = R / 4$.
$(b)$ When these four parts are connected in parallel, the equivalent resistance becomes
$\frac{1}{ R _{ P }}=\frac{1}{ R _{1}}+\frac{1}{ R _{2}}+\frac{1}{ R _{3}}+\frac{1}{ R _{4}}$
$=\frac{4}{R}+\frac{4}{R}+\frac{4}{R}+\frac{4}{R}=\frac{16}{R}$
Hence, $R _{ p }=16 ohm$
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