Topic 11.4 Notes – Electric Power

1. What Electric Power Is in a Circuit

Electric power is the rate of energy transfer.

$$P = \frac{E}{t}$$

• Unit: watt (W)
• $1 \text{ W} = 1 \text{ J/s}$

So if a device has a power of 60 W, it transfers 60 joules of energy every second.

In a circuit:

• The battery transfers energy to the charges.
• Charges carry that energy through the wires.
• Circuit elements (bulbs, resistors, motors) convert that electrical energy into:
  • Thermal energy (resistors)
  • Light (bulbs)
  • Mechanical energy (motors)
  • Sound, etc.

A component with larger power is transferring energy faster. That’s the whole meaning.

Power depends on current and voltage

The rate of energy transfer in any circuit element depends on:

• The current $I$ through it (charge per second)
• The potential difference $\Delta V$ across it (energy per charge)

Multiply them together:

$$P = I \Delta V$$

This is the most fundamental power equation.

Think of it this way:

• Current tells you how much charge flows each second.
• Voltage tells you how much energy each coulomb carries.
• Multiply → energy per second.

2. The Power Equations You Must Know

Using Ohm’s law, $\Delta V = IR$, we can rewrite $P = I\Delta V$ in two other forms.

Three equivalent equations

$$P = I\Delta V$$

$$P = I^{2} R$$

$$P = \frac{(\Delta V)^{2}}{R}$$

They are all the same relationship, just rearranged.

When each form is useful

• Same current known? Use $P = I^{2}R$
• Same voltage known? Use $P = \frac{V^{2}}{R}$
• Know both I and V? Use $P = IV$

Important pattern (with constant resistance):

• If current doubles → power becomes 4 times larger.
• If voltage doubles → power becomes 4 times larger.

That squared relationship shows up a lot in brightness comparisons.

3. Power in Different Circuit Elements

Resistors

In a resistor:

$$P = I^{2}R$$

The energy is converted into thermal energy. That’s why resistors heat up.

If current increases even a little, heating increases dramatically because of the square.

This is why overloaded circuits get hot.

Light Bulbs

For identical bulbs:

Brightness is proportional to power.

More power → more energy per second → more light.

If two identical bulbs have different powers, the one with greater power is brighter. On exams, you usually don’t need exact numbers. You compare which one has larger $P$.

Batteries

For a battery with emf $\varepsilon$:

$$P = I\varepsilon$$

This is the rate at which the battery supplies energy.

In a steady-state circuit:

Total power supplied by the battery = total power dissipated in the circuit.

That’s energy conservation written in power language.

4. Predicting Brightness in Series and Parallel Circuits

The trick is to combine circuit rules with power equations.

First remember:

• Series → same current through each element.
• Parallel → same voltage across each branch.

Here’s a quick visual reminder for series circuits. As more identical bulbs are added in series with the same battery, each one becomes dimmer.

Identical bulbs added in series with one battery

Identical bulbs comparison

For identical bulbs:

• In series, each bulb gets less voltage than the battery provides, so each has lower power.
• In parallel, each bulb gets the full battery voltage, so each has the same power as a single bulb alone.

If you ever get stuck:

1. Decide whether current or voltage is the same.
2. Choose the matching power formula.
3. Compare powers.
4. Larger power = brighter bulb.