An electric current of 2.0\,\text{A} flows through a resistor of resistance 5.0\,\Omega fo… — JAMB UTME

An electric current of $2.0\,\text{A}$ flows through a resistor of resistance $5.0\,\Omega$ for a duration of $10.0\,\text{seconds}$ . What is the total electrical energy, in Joules, dissipated by the resistor?

Answer: 200 J

Answer

The total electrical energy dissipated by the resistor is

200\,\text{J}

According to Joule's law of heating, the electrical energy

E

converted into thermal energy when a current

I

flows through a resistor

R

for time

t

is given by

E = I^2 R t

. Substituting

I = 2.0\,\text{A}

R = 5.0\,\Omega

, and

t = 10.0\,\text{s}

gives

E = (2.0)^2 \times 5.0 \times 10.0 = 4.0 \times 5.0 \times 10.0 = 200\,\text{J}

Step-by-Step Solution

Identify the given physical values from the problem statement.

I = 2.0\,\text{A}

R = 5.0\,\Omega

t = 10.0\,\text{s}

These are the necessary parameters to compute electrical energy.

State the formula for electrical energy dissipated in a resistor (Joule's law).

E = I^2 R t

Electrical energy is equal to power multiplied by time, where power

P = I^2 R

Calculate the numerical value of the energy.

E = (2.0)^2 \times 5.0 \times 10.0 = 200\,\text{J}

Squaring the current gives

4.0\,\text{A}^2

, and multiplying by

5.0\,\Omega

and

10.0\,\text{s}

yields

200\,\text{J}

Key Concept

Joule's Law of Electrical Heating

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