Problem 80 - A Complete Resource Book in Physics for JEE Main

Question

The resistance of a wire is \(10 \Omega\). Its length is increased by \(10 \%\) by stretching. The new resistance will now be nearly (A) \(12 \Omega\) (B) \(1.2 \Omega\) (C) \(13 \Omega\) (D) \(11 \Omega\)

Step-by-Step Solution

Answer

The new resistance remains \(10 \Omega\). (None of the given options)

Step 1: Determine the Initial Resistance

The initial resistance is given as \(R = 10 \Omega\). No calculations are necessary for this step.

Step 2: Calculate the changed length and area

The length is increased by 10%, hence the new length is \(L' = 1.10L\). Since volume remains unchanged, if length increases by 10%, area decreases by the same percent to maintain the constant volume. Thus, the new area \(A' = 0.90A\).

Step 3: Calculate the New Resistance

Now, substitute new values of length and area into the resistance formula \(R = \rho\frac{L'}{A'}\). Since resistance is proportional to length and inversely proportional to area, and both length and area have changed by 10%, these changes will cancel out. Hence, the new resistance \(R' = R = 10 \Omega\).