Question

A copper wire of resistance R is cut into ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have a resistance

• A. R
• B. $\frac{R}{4}$
• C. $\frac{R}{5}$
• D. $\frac{R}{25}$

Answer 1

Answer: (D)

$\frac{R}{25}$

Answer 2

$R \propto l$

Hence every new piece will have a resistance $\frac{R}{10}.$

If two pieces are connected in series, then their resistance $= \frac{2R}{10} = \frac{R}{5}$

If 5 such combinations are joined in parallel, then net resistance $= \frac{R}{5 \times 5} = \frac{R}{25}$