Question

You are given several identical resisters each of value of $5\Omega$ and each capable of carrying a maximum current of $2A$. It is required to make a suitable combination of these resistances to produce a resistance of $2.5\Omega$ which can carry current of $4A$. The minimum number of resistances required for this job is

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is D $8$

Solution:

Here we need four parallel paths, each carrying a current of $1A$. If R s the resistance of each path, then the equivalent resistance of the combination is $\frac{R}{4}$

And as per given criteria, $\frac{R}{4}=5\Omega ⟹R=20\Omega$

Therefore, two resistors should be connected in each path as shown in the above figure. Hence Total number of resistors = 8