Power in Circuits

Power in a circuit tells you how fast electrical energy is being converted into other forms — usually heat (toaster, hair dryer), light (bulb), or motion (motor). When you pay your electricity bill, you’re literally paying for power × time = energy.

The MCAT tests circuit power with three equivalent formulas. The trick isn’t memorizing any one of them — it’s knowing which form to reach for depending on what the question gives you.

The Three Power Formulas

When to use each:

• $P = IV$ — when you know current and voltage directly.
• $P = I^2R$ — when you know current and resistance. Common in series circuits, where current is the same through every resistor.
• $P = V^2/R$ — when you know voltage and resistance. Common in parallel circuits, where voltage is the same across every resistor.

Brightness of Bulbs

The MCAT loves asking which bulb in a circuit is brightest. The rule is simple:

Brightness ∝ power dissipated by the bulb.

But which power formula to use depends on the configuration:

• In a series circuit, all bulbs carry the same current. So $P = I^2R$ — the bulb with the highest resistance is brightest.
• In a parallel circuit, all bulbs see the same voltage. So $P = V^2/R$ — the bulb with the lowest resistance is brightest.

Energy Dissipated

Power is energy per unit time. To find total energy dissipated by a resistor over a time $t$:

This is exactly how electricity bills work — you pay for energy in kilowatt-hours (kWh), not power. A 100 W bulb running 10 hours = 1 kWh ≈ 15¢.

RMS Values (AC Circuits)

The MCAT occasionally touches on alternating current (AC). In AC circuits, voltage and current oscillate sinusoidally — they’re constantly changing direction. To get a meaningful “average” power, we use root-mean-square (RMS) values.

The average power dissipated in an AC circuit uses RMS values: $P_{avg} = I_{rms} V_{rms} = I_{rms}^2 R$.