# Activity: Electrical power

#### Aims

- Derive the formula P = IV
- Measure the electrical power for different examples
- Estimate power loss in cables.
- Have an idea of magnitudes of domestic electrical power usage

#### Power converted by the battery

- What is the definition of EMF?
- How much chemical energy is converted to electrical PE when charge q flows in the battery?
- If charge q flows in time t what is the power delivered by the battery?

You should now understand why the power delivered by the battery is given by:

P = εI

#### Power dissipated in a resistor

- What is the definition of potential difference across a resistor?
- How much electrical energy is converted to heat when charge q flows?
- If charge q flows in time t what is the power dissipated in the resistor?

So power dissipated is give by:

P = IV

From Ohm's law V = IR.

- Substitute for V to give an equation in terms of I and R.
- Substitute for I to give an equation in terms of V and R.

#### Measuring power

__Electric kettle__

An electric kettle converts electrical energy into heat.

- Use a temperature sensor to measure the rate of temperature rise for an electric kettle and calculate the power delivered to the water.
- How does your value compare to the makers value?

__Light bulb__

A light bulb converts electrical energy into light but also produces heat.

- Use the special "light bulb in water" apparatus to measure how much energy is converted to heat per unit time.
- Measure the current through and pd across the light bulb and calculate the power dissipated.
- Calculate the % of electrical energy converted to light per second.

__Electric motor__

An electric motor converts electrical energy to mechanical energy

- Devise a method for measuring the power of a battery power drill. Discuss the method with your teacher and if possible perform the experiment.

__Heat loss in cables__

Ideal wires have zero resistance, real ones don't

- Measure the resistance of the cable connecting the kettle to the mains supply. The cable must be disconnected from the mains supply when you do this.
- Calculate the heat loss per second in the cable when the kettle is in use.

If too much heat is generated in a cable it will get hot and the insulator will melt.

DO NOT TRY THIS!

Different electrical devices need different amounts of current.

- Use the "power meter" to measure the power of different devices.
- Is there a relationship between the power of the device and the thickness of the cable?

When wiring a house some devices need more power than others so different cables must be used. To protect the cables from overload a circuit breaker is installed, this will switch off if the current becomes too big for the cables. Have a look in the switch cupboard.

- What is the current value for the largest circuit breaker?
- What sort of devices are connected to this circuit?
- What sort of device is the lowest current circuit used for?
- Estimate the total current that can be supplied.
- Calculate the maximum power that could be delivered.
- Electrical energy is measured in kWh, how many Joules is equivalent to 1 kWh?

__Batteries__

The total amount of energy that can be convert from chemical to electrical during the life of a battery can be calculated from the Ah (Amp hour) rating. A 1 Ah rating means the battery can deliver 1 A for 1 hour. A typical 1.5 V AA has a rating of about 2 Ah.

- Calculate the total energy that can be delivered by an AA battery (in Joules).
- Find out the rating of different makes of battery. Do the expensive ones contain more energy?

Exercises on page 228 - 229