Question

In the equation AB = C, A is the current density, C is the electric field, Then B is

• A. Conductivity
• B. Resistance
• C. potential difference
• D. Resistivity

Answer 1

The Correct Option is D

To solve the problem, we need to determine what physical quantity B represents in the equation AB = C, where A is the current density and C is the electric field.

1. Understanding the Given Quantities:
We are given:
- A = Current density (J) with units A/m²
- C = Electric field (E) with units V/m
- The equation relating them: AB = C

2. Dimensional Analysis:
Let's analyze the units of the equation:

J × B = E
(A/m²) × [B] = V/m
Therefore, the units of B must be:

[B] = (V/m)/(A/m²) = V·m/A

3. Relating to Known Physical Quantities:
The unit V·m/A is equivalent to Ω·m (ohm-meter), which is the unit of:
- Electrical resistivity (ρ)
This comes from the microscopic form of Ohm's Law:

E = ρJ

4. Comparing with Given Equation:
Our given equation is:
AB = C → JB = E
Ohm's Law states:
E = ρJ
Therefore, we can conclude:

B = ρ

5. Verification:
Let's verify the units:
- ρ has units of Ω·m
- Our dimensional analysis showed B must have units of V·m/A
Since 1 Ω = 1 V/A, the units match perfectly.

Final Answer:
B represents the resistivity (ρ) of the material.