Match each electrical quantity or operational scenario on the left with its corresponding … — JAMB UTME

Match each electrical quantity or operational scenario on the left with its corresponding mathematical expression on the right.

Electrical power dissipated in a resistor of resistance $R$ carrying current $I$ $I^2 R$
Electrical energy consumed by a device of resistance $R$ operating across potential difference $V$ for duration $t$ $\frac{V^2 t}{R}$
Rate of heat generation in a component operating with potential difference $V$ and current $I$ $V I$
Total electric charge transferred across a potential difference $V$ when electrical energy $E$ is transformed $\frac{E}{V}$

Electrical power in terms of current and resistance corresponds to

I^2 R

. Electrical energy consumed across voltage

V

for time

t

corresponds to

\frac{V^2 t}{R}

. Rate of heat generation in terms of voltage and current corresponds to

V I

. Total electric charge transformed corresponds to

\frac{E}{V}

Each item is matched by applying the fundamental relationships of electrical energy (

E = V I t = I^2 R t = \frac{V^2 t}{R} = Q V

) and electrical power (

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

Analyze the first scenario (power with current and resistance)

Power formula derived from Ohm's law (

V = IR

) into

P = VI

gives

P = (IR)I = I^2 R

Relates current and resistance directly to power dissipation.

Analyze the second scenario (energy with voltage, resistance, and time)

Energy

E = P t

. Using

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

, energy becomes

E = \frac{V^2 t}{R}

Expresses energy consumption using voltage and resistance over a given time duration.

Analyze the third scenario (rate of heat generation with voltage and current)

Rate of heat generation is power

P = V I

Direct definition of electrical power as energy converted per unit time.

Analyze the fourth scenario (charge transferred from energy and voltage)

Since potential difference is energy per unit charge (

V = \frac{E}{Q}

), rearranging gives

Q = \frac{E}{V}

Relates fundamental definitions of potential difference, energy, and charge.

Formulas for Electrical Energy, Power, and Charge

Question