Question

Resistance R, 2R, 3R ...NR if, NR ..............$\infty$ are connected in parallel. Their resultant resistance will be

• A. R
• B. R/2
• C. 0
• D. $\infty$

Answer 1

Answer: (C)

0

The equivalent resistance of N resistors connected in parallel connection is given by,
$\frac{1}{R_{Equivalent}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_N}$
Substituting respective values,
$\frac{1}{R_{Equivalent}}=\frac{1}{R}+\frac{1}{2R}+\frac{1}{3R}+...+\frac{1}{NR}$

The R.H.S. diverge as N $\to \infty$
Hence,
$R_{Equivalent}=0$