A wire of resistance R has it length and cross-section both doubled. Its resistance will become
A
4 R
B
2 R
C
R
D
R / 4

Question

A wire of resistance R has it length and cross-section both doubled. Its resistance will become

Examoogle · Accepted Answer

R

Explanation: Given: Initial resistance is R, length is doubled (l_2 = 2l_1), and cross-sectional area is doubled (A_2 = 2A_1).

Formula Used: $$R = \rho \frac{l}{A}$$

Steps: Define the initial resistance: The resistance of a wire is given by $R_1 = \rho \frac{l_1}{A_1}$, where $\rho$ is the resistivity, $l_1$ is the length, and $A_1$ is the cross-sectional area.. Define the final resistance: With the new dimensions $l_2 = 2l_1$ and $A_2 = 2A_1$, the new resistance $R_2$ is calculated as $R_2 = \rho \frac{l_2}{A_2}$.. Simplify and compare: Substituting the new dimensions into the formula, we see that the factor of 2 in both the numerator and denominator cancels out.

Answer: C is correct because doubling both length and area results in the resistance remaining unchanged at R.

Exam Tip: This principle is often used in transformer winding design where changing the wire gauge (area) alongside turns (length) must be balanced to maintain specific resistance characteristics.

Related Questions

Discussion (0)