A cylindrical copper rod has resistance R.It is reformed to twice its original length with no change of volume.Its new resistance is:
A)R/2
B)R
C)2R
D)4R
E)8R

Question

Quizplus · Accepted Answer

The resistance $R$ of a cylindrical conductor (like a copper rod) is given by $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity of the material, $L$ is the length, and $A$ is the cross-sectional area. When the rod is stretched to twice its original length without changing its volume, its cross-sectional area $A$ is halved (since volume $V = A \cdot L$ remains constant and $L$ is doubled). The new resistance $R'$ can be calculated as $R' = \rho \frac{2L}{A/2} = 4 \rho \frac{L}{A} = 4R$, indicating that the resistance becomes four times the original resistance.

A Cylindrical Copper Rod Has Resistance R