A potential difference of 16\,\text{V} is applied across a uniform conductor of length 4.0… — JAMB UTME

A potential difference of $16\,\text{V}$ is applied across a uniform conductor of length $4.0\,\text{m}$ and cross-sectional area $1.5 \times 10^{-6}\,\text{m}^2$ . If the resistivity of the conductor material is $3.0 \times 10^{-7}\,\Omega\cdot\text{m}$ , what is the electric current, in amperes, flowing through the conductor?

Answer: 20 A

Answer

The electric current flowing through the conductor is

20\,\text{A}

The electrical resistance of the wire is first determined using the formula

R = \frac{\rho L}{A} = \frac{(3.0 \times 10^{-7})(4.0)}{1.5 \times 10^{-6}} = 0.8\,\Omega

. Then, by applying Ohm's law (

I = \frac{V}{R}

), the current is computed as

I = \frac{16}{0.8} = 20\,\text{A}

Step-by-Step Solution

Calculate the electrical resistance of the conductor from its physical dimensions and resistivity.

R = 0.8\,\Omega

Substitute

\rho = 3.0 \times 10^{-7}\,\Omega\cdot\text{m}

L = 4.0\,\text{m}

, and

A = 1.5 \times 10^{-6}\,\text{m}^2

into

R = \frac{\rho L}{A}

Apply Ohm's law to calculate the current flowing through the conductor.

I = 20\,\text{A}

Substitute potential difference

V = 16\,\text{V}

and calculated resistance

R = 0.8\,\Omega

into

I = \frac{V}{R}

Key Concept

Relationship between resistivity, resistance, potential difference, and electric current

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