Match each electrical scenario or description in List I with its corresponding mathematica… — JAMB UTME

Match each electrical scenario or description in List I with its corresponding mathematical expression or unit in List II.

Energy dissipated by a resistor of resistance $R$ carrying current $I$ for duration $t$ $I^2 R t$
Power rating of an appliance of resistance $R$ operating under voltage $V$ $\frac{V^2}{R}$
Commercial unit of electrical energy equal to $3.6 \times 10^6\,\text{J}$ 1 kWh
Rate of heat production in a component with potential difference $V$ and current $I$ $I V$

Answer

The correct pairings are: Energy dissipated in duration

t

matches

I^2 R t

; Power rating under voltage

V

matches

\frac{V^2}{R}

; Commercial unit equal to

3.6 \times 10^6\,\text{J}

matches 1 kWh; Rate of heat production matches

I V

Each description in List I corresponds directly to its standard physical formula or commercial unit in List II based on the definitions of electrical power (

P = I V = \frac{V^2}{R}

) and electrical energy (

E = I^2 R t = P t

Step-by-Step Solution

Identify Joule's law of heating for energy dissipation over time.

Energy

E = I^2 R t

, matching the expression

I^2 R t

Joule's heating effect states that electrical energy transformed into heat energy is directly proportional to

I^2

R

, and

t

Relate power, voltage, and resistance.

Power

P = \frac{V^2}{R}

, matching the expression

\frac{V^2}{R}

Substituting Ohm's law

I = \frac{V}{R}

into power formula

P = I V

yields

P = \frac{V^2}{R}

Convert kilowatt-hours to joules for commercial unit matching.

1\,\text{kWh} = 1000\,\text{W} \times 3600\,\text{s} = 3.6 \times 10^6\,\text{J}

, matching 1 kWh.

Kilowatt-hour is the standard energy unit used by electric utility companies.

Determine the general definition of electrical power as the rate of energy transfer.

Power

P = I V

, matching the expression

I V

Electric power is defined as the product of current

I

and potential difference

V

Key Concept

Formulas and units for electrical energy, electric power, Joule's law of heating, and kilowatt-hours.

Estimated Time:1m 30s

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