Question

A wire of diameter 2.3 mm carries 4.2 A current. Connected in parallel with this wire is a second wire of the same material and of equal length but of diameter 5.1 mm. What is the current density in the second wire?(Take $\pi$ = 3.14)

• A. 1.01 x $10^6$ A/m²
• B. 2.02 x $10^6$ A/m²
• C. 0.51 x $10^6$ A/m²
• D. 0.71 x $10^6$ A/m²

Answer 1

Answer: (A)

1.01 x $10^6$ A/m²

Answer 2

The key to this problem is recognizing that since the wires are in parallel, made of the same material, and have the same length, the current density will be the same in both wires. Therefore, we only need to calculate the current density in the first wire.

Current density, $J$, is given by $J = \frac{I}{A}$, where $I$ is the current and $A$ is the cross-sectional area.

1. Calculate the cross-sectional area of the first wire:

   $A_1 = \frac{\pi d_1^2}{4} = \frac{3.14 \times (2.3 \times 10^{-3} \text{ m})^2}{4} \approx 4.15265 \times 10^{-6} \text{ m}^2$

2. Calculate the current density in the first wire:

   $J_1 = \frac{I_1}{A_1} = \frac{4.2 \text{ A}}{4.15265 \times 10^{-6} \text{ m}^2} \approx 1.01 \times 10^6 \text{ A/m}^2$

Since $J_1 = J_2$, the current density in the second wire is also approximately $1.01 \times 10^6 \text{ A/m}^2$.