Electrical work

fig A As part of this circuit, the heart will convert some electrical energy into kinetic energy. The circuit is doing work.

The measurement of voltages in electric circuits has shown us that these deal with the conversion of energy by components. Energy must always be conserved, and electric circuits are no exception to this. When components convert electrical energy into other useful forms, they can be considered to be doing work, as this is defined as a transfer of energy.  

The equation for potential difference, in rearranged form, gives us: Table 1. Equation for work

Equation	Symbol	Units
	W=work	Joules (J)
	V=potential difference	Volts (V)
	q=electric charge	Coulombs (C)

The definition of current, in rearranged form, is the equation   Table 2. Equation for charge

Equation	Symbol	Units
	q=electric charge	Coulombs (C)
	I=current	Amperes (A)
	t=time	Seconds (s)

Combining these will give us the work done by a component in an electric circuit: Table 3. Equation for work

Equation	Symbol	Units
	W=work	Joules (J)
	V=potential difference	Volts (V)
	I=current	Amperes (A)
	t=time	Seconds (s)

Worked example 1Worked example 2

In fig B, If the bulb lights up for 4.85 seconds, how much work has the bulb done?

Step 1: Identify the given information. t = 4.85 J V = 7.06 V I = 1.45 A Step 2: Identify the missing variable. W= ?

Step 3: State the formula Step 4: Substitute the values and calculate. W=49.6 J

A student sets up a circuit using a power supply. The voltmeter in the circuit reads 12.0 V, and the ammeter reads a current of 2.5 A. If the circuit does 4500 J of electrical work while the light bulb is on, how long was the power supply running? Give your answer in seconds and minutes.   Step 1: Identify the given information. W = 4500 J V = 12.0 V I = 2.5 A Step 2: Identify the missing variable. t= ? Step 3: State the formula and rearrange it. The standard formula is: To isolate t: Step 4: Substitute the values and calculate. t=150s=2.5 min Sources:

1. Hudson, M. (2015). Edexcel AS/A level physics 1. Pearson Education Limited.
2. Gemini. (2025). Response to a prompt to draw an electric circuit and create a working example. https://gemini.google.com/

Power

Power, P, is the rate of transfer of energy, or the rate of doing work. In an electrical circuit, the energy is dissipated by a component. The mathematical definition is: Table 1. Equation for power

Equation	Symbol	Units
	W=work	Joules (J)
	t=time	Seconds (s)
	P=power	Watts (W)

Incorporating the equation for work in a circuit from above: Table 2. Equation for power

Equation	Symbol	Units
	P=power	Watts (W)
	V=potential difference	Volts (V)
	I=current	Amperes (A)

Cost of electricity

The electricity board metres in homes, offices and other buildings show how much electricity was used in the building. Readings on the meter (fig 1)  give the total amount of energy supplied in “units”. The board meters use kilowatt-hours (kW-h) as the unit of electrical energy. The Electricity Board determines the price for each unit. To calculate the cost of electricity, the price per unit is multiplied by the total amount of electricity used:

Cost of the electricity in the World

https://worldpopulationreview.com/country-rankings/cost-of-electricity-by-country

Worked example 1Worked example 2Worked example 3

A toaster is connected to a 220 V supply and draws a current of 3 A for 10 s. Calculate the electrical work done. Problem: A toaster is connected to a 220 V supply and draws a current of 3 A. Calculate its power. Step 1: Identify the given information 𝑉=220V 𝐼=3A Step 2: Identify the missing variable 𝑃=? Step 3: State the formula Step 4: Substitute the values and calculate P=220*3=660 W

A 100 Ω resistor is connected to a 12 V battery. Calculate the electrical power. Step 1: Identify the given information 𝑉=12 V 𝑅=100Ω Step 2: Identify the missing variable 𝑃=? Step 3: State the formula Step 4: Substitute the values and calculate P=1.44 W

An electric heater with a power of 2 kW is used for 5 hours per day for 30 days. The electricity tariff is 25 KZT per kWh. Calculate the total cost of electricity. Step 1: Identify the given information P=2kW t=5h/day*30days=150h Tariff=25 KZT /kWh Step 2: Identify the missing variable Cost=? Step 3: State the formula Step 4: Substitute the values and calculate E=2×150=300 kWh Cost=300×25 Cost=7500 KZT   Sources:

1.  Hudson, M. (2015). Edexcel AS/A level physics 1. Pearson Education Limited.
2.  Gemini. (2025). Response to a prompt to create a working example. Google. https://gemini.google.com/
3. Zambak Publications. (n.d.). Physics: Electricity and magnetism. Zambak Publishing.

Practice