An aluminium wire of diameter 0.24 cm is connected in series to a copper wire of diameter 0.16 cm. The wires carry an electric current of 10 A. Determine the current density in aluminium wire.

To find the current density in the aluminium wire, we first need to calculate its cross-sectional area. The formula for the area \( A \) of a wire with a circular cross-section is given by:

Calculating the Cross-Sectional Area

The area can be calculated using the formula:

A = πr²

where \( r \) is the radius of the wire. Since the diameter of the aluminium wire is 0.24 cm, we can find the radius:

• Radius \( r = \frac{diameter}{2} = \frac{0.24 \, \text{cm}}{2} = 0.12 \, \text{cm} = 0.0012 \, \text{m}\)

Now, substituting the radius into the area formula:

A = π(0.0012 m)² ≈ 4.52 × 10⁻⁶ m²

Finding the Current Density

Current density \( J \) is defined as the current \( I \) flowing through a unit area \( A \) of the wire:

J = I / A

Given that the current \( I \) is 10 A, we can now calculate the current density:

• J = 10 A / 4.52 × 10⁻⁶ m² ≈ 2.21 × 10⁷ A/m²

Final Result

The current density in the aluminium wire is approximately 2.21 × 10⁷ A/m².