Question

You are given $10$ resistors each of resistance $2\Omega$. First they are connected to obtain possible minimum resistance. Then they are connected to obtain possible maximum resistance. The ratio of maximum and minimum resistance is _________.

• A. $100$
• B. $10$
• C. $2.5$
• D. $25$

Answer 1

The correct option is A $100$

Given : $R=2\Omega$ $n=10$
Minimum resistance is obtained when all the 10 resistors are connect in parallel.
Minimum resistance $R_{min}=\frac{R}{n}=\frac{2}{10}=0.2\Omega$
Maximum resistance is obtained when all the 10 resistors are connect in series.
Maximum resistance $R_{max}=nR=10\times 2=20\Omega$
Ratio of maximum to minimum resistance $\frac{R_{max}}{R_{min}}=\frac{20}{0.2}=100$