If a person has five resistors each of value $\frac {1}{5}\Omega$, then the maximum resistance he can obtain by connecting them is(A) 1W (B) 5W (C) 10W (D) 25W
(A) 1W
Explanation
We know that total resistance decreases when resistors are connected in parallel.
It is calculated as $\frac{1}{{R}_{T}}=\frac{1}{{R}_{1}}+\frac{1}{{R}_{2}}+\frac{1}{{R}_{3}}+\frac{1}{{R}_{4}}+........+\frac{1}{Rn}$
While total resistance increases when resistors are connected in series.
It is calculated as ${R}_{T}={R}_{1}+{R}_{2}+{R}_{3}+{R}_{4}+........+{R}_{n}$
It means, we can get minimum resistance when all the given resistors will join in parallel, and maximum resistance can be obtained when all the given resistors will join in series.
So, for finding maximum resistance, we have to join all resistors in series.
Here, given 5 resistors each of resistance $\frac{1}{5}\Omega $ or $0.2\Omega $.
Now, putting the value of the resistors in the formula of series connection-
${R}_{T}= 0.2 + 0.2 + 0.2 + 0.2 + 0.2 $
${R}_{T}= 1.0\Omega $
Hence, maximum resistance which can be made using five resistors each of $\frac{1}{5}\Omega $ is $1\Omega $.
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