Question

A conductor of non uniform cross section is connected across a potential difference V as shown in the figure, Choose the correct option regarding the conductor :

• A. current at B is same as that of A
• B. current density near at the end A inside the conductor is more than the current density near the end B inside the conductor
• C. resistance of thickness dx near the end B is less than the resistance near the end A
• D. electric field near the end A is more than at B

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A current at B is same as that of A
B current density near at the end A inside the conductor is more than the current density near the end B inside the conductor
C resistance of thickness dx near the end B is less than the resistance near the end A
D electric field near the end A is more than at B

By law of conservation of charge, current is constant across all the cross sections of the resistor. Hence, current at A is same as current of B.

Current density is given by, $J=\frac{I}{A}$. Since current is constant, current density at A is more than current density at B.

Resistance of a cross-section of dx thickness is given by, $dR=\frac{\rho dx}{A}$. Resistivity is same for the material and $dx$ is same for all cross sections, hence resistance at A is more than resistance at B.

From alternative form of ohm's law, $J=\sigma E$

Hence, electric field at end A is more than the electric field at end B.