An electric immersion heater with a resistance of 20\,\Omega carries a steady current of 3… — JAMB UTME

An electric immersion heater with a resistance of $20\,\Omega$ carries a steady current of $3\,\text{A}$ . How much electrical energy is dissipated as heat by the heater in $10\,\text{seconds}$ ?

A
$600\,\text{J}$
B
$1200\,\text{J}$
$1800\,\text{J}$ Answer
D
$180\,\text{J}$

Answer

The total electrical energy dissipated as heat by the heater is

1800\,\text{J}

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

E

converted into heat energy in a resistor is given by

E = I^2 R t

. Substituting

I = 3\,\text{A}

R = 20\,\Omega

, and

t = 10\,\text{s}

yields

E = (3)^2 \times 20 \times 10 = 9 \times 200 = 1800\,\text{J}

Step-by-Step Solution

Identify the given physical quantities

Resistance

R = 20\,\Omega

, Current

I = 3\,\text{A}

, Time

t = 10\,\text{s}

Recognize the required values needed to compute heat energy dissipated in a resistor.

Select the appropriate formula for heat energy

E = I^2 R t

Joule's Law of Heating relates electrical energy, current, resistance, and time.

Substitute the known values into the equation and calculate

E = (3)^2 \times 20 \times 10 = 9 \times 20 \times 10 = 1800\,\text{J}

Perform arithmetic multiplication to find the final heat energy in Joules.

Key Concept

Joule's Law of Heating

Question

Answer

Step-by-Step Solution

Key Concept

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