Question

A wire of uniform cross-section and length $l$ has a resistance of $16 \Omega$. It is cut into four equal parts. Each part is stretched uniformly to length $l$ and all the stretched parts are connected in parallel. Calculate the total resistance of the combination so formed. (Assume that the stretching of the wire does not cause any change in the density of the material.)

• A. $10\, \Omega$
• B. $12 \, \Omega$
• C. $16\, \Omega$
• D. $18\, \Omega$

Answer 1

Answer: (C)

In stretching 4 times $R$ becomes $4^{2}$ time
$R^{\prime}=\frac{R}{4}=\frac{16}{4}=4 $
$R^{\prime \prime}=4^{2} \times 4=64$
Each part has $\frac{1}{R_{ eq }}=\frac{1}{64}+\frac{1}{64}+\frac{1}{64}+\frac{1}{64}=\frac{4}{64}$
$R_{ eq }=16 \Omega$