Question

A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is $R^{{}^{\prime }}$, then the ratio $\frac{R}{R^{{}^{\prime }}}$ is :

• A. 1/25
  
• B. 25
• C. 1/5
• D. 5

Answer 1

The correct option is B

25

When we divide resistance wire in equal ratio the resistance value of each wire is also divided in that ratio. As in this case length of each new wire has reduced but cross section area and resistivity is the same. So the resistance of each wire is ${\frac{1}{5}}^{th}$ of the original wire, which is equal to $\frac{R}{5}$

Now these wires are in parallel. So the net resistance is given by

$\frac{1}{R^{{}^{\prime }}}$= $\frac{5}{R}$ +$\frac{5}{R}$+$\frac{5}{R}$+$\frac{5}{R}$+$\frac{5}{R}$

R’ = $\frac{R}{25}$

$\frac{R}{R^{{}^{\prime }}}$ = 25