Question

A uniform wire of resistance R and length L is cut into four equal parts, each of length $L/4$, which are then connected in parallel combination. The effective resistance of the combination will be

• A. R
• B. 4R
• C. $\frac {R}{4}$
• D. $\frac {R}{16}$

Answer 1

The Correct Option is D

Resistance $R=\frac {pl}{A}$ or $R ? l$
$\therefore$ $\hspace30mm$ $\frac {R_1}{R_2}=\frac {l_1}{l_2}=\frac {L}{L/4}=4$
or $\hspace30mm$ $R_2=\frac {R}{4}$ $\hspace30mm$ ($\because R_1=R$)
In parallel combination of such four resistances.
$\frac {1}{R'}=\frac {1}{R_2}+\frac {1}{R_2}+\frac {1}{R_2}+\frac {1}{R_2}$
or $\hspace30mm$ $\frac {1}{R'}=\frac {1}{R/4}+\frac {1}{R/4}+\frac {1}{R/4}+\frac {1}{R/4}$
or $\hspace30mm$ $\frac {1}{R'}=\frac {4}{R}+\frac {4}{R}+\frac {4}{R}+\frac {4}{R}$
or $\hspace30mm$ $\frac {1}{R'}=\frac {16}{R}$ or $R'=\frac{R}{16}$