Transformer Power Equation

The Principle of an Ideal Transformer

Think about the plug heating up when you charge your phone—that wasted heat means real chargers are not perfectly efficient.
However, in physics, we often start by assuming an ideal transformer where absolutely no energy is lost to the iron core or surroundings as heat.
This theoretical model operates at 100% efficiency, meaning the exact amount of power entering the device is equal to the power leaving it.
This concept relies entirely on the fundamental Law of Conservation of Energy, which states that energy cannot be created or destroyed.

The Power Equation

We can express this conservation of energy mathematically. Electrical power ( $P$ ) is the rate of energy transfer, calculated by multiplying the potential difference ( $V$ ) by the current ( $I$ ).
Because the power entering the primary coil must equal the power leaving the secondary coil, we can state that Power in = Power out.

V_p \times I_p = V_s \times I_s

Where:

$V_p$ = potential difference across the primary coil (in Volts, V)
$I_p$ = current in the primary coil (in Amps, A)
$V_s$ = potential difference across the secondary coil (in Volts, V)
$I_s$ = current in the secondary coil (in Amps, A)

The Inverse Relationship

Because the total power remains constant across a 100% efficient transformer, potential difference and current must be inversely proportional.
In a step-up transformer, the potential difference increases ( $V_s > V_p$ ), so the current must decrease proportionally ( $I_s < I_p$ ).
In a step-down transformer, the potential difference decreases ( $V_s < V_p$ ), so the current must increase ( $I_s > I_p$ ).
This inverse relationship is exactly why the National Grid transmits electricity at extremely high potential differences. Stepping up the potential difference means a much lower current, which drastically reduces the amount of energy wasted as heat in transmission wires.
Note that this process only works because transformers are supplied with an alternating current (AC), which creates the changing magnetic field needed to induce a potential difference.

Worked Example: Calculating Current

A step-up transformer at a power station is assumed to be 100% efficient. It takes an input potential difference of $20,000\text{ V}$ and steps it up to $400,000\text{ V}$ for transmission. If the current in the primary coil is $5,000\text{ A}$ , calculate the current in the secondary coil.

Step 1: State the formula and identify the known values.

$V_p \times I_p = V_s \times I_s$
$V_p = 20,000\text{ V}$ , $V_s = 400,000\text{ V}$ , $I_p = 5,000\text{ A}$

Step 2: Substitute the values into the equation.

$20,000 \times 5,000 = 400,000 \times I_s$

Step 3: Rearrange to solve for $I_s$ .

$100,000,000 = 400,000 \times I_s$
$I_s = \frac{100,000,000}{400,000}$

Step 4: Calculate the final answer with units.

$I_s = 250\text{ A}$

Worked Example: Calculating Potential Difference

A laptop charger uses a step-down transformer to convert a $230\text{ V}$ mains a.c. supply into a safe output for the battery. The primary current is $0.15\text{ A}$ and the secondary current is $2.3\text{ A}$ . Assuming 100% efficiency, calculate the potential difference across the secondary coil.

Step 1: State the formula and identify the known values.

$V_p \times I_p = V_s \times I_s$
$V_p = 230\text{ V}$ , $I_p = 0.15\text{ A}$ , $I_s = 2.3\text{ A}$

Step 2: Substitute the values into the equation.

$230 \times 0.15 = V_s \times 2.3$

Step 3: Rearrange to solve for $V_s$ .

$34.5 = V_s \times 2.3$
$V_s = \frac{34.5}{2.3}$

Step 4: Calculate the final answer with units.

$V_s = 15\text{ V}$

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Exam Tips

Common Mistake
Students often use the word 'voltage' in their written answers, but Edexcel explicitly prefers and awards marks for the term 'potential difference'.
2
In calculation questions, always write down your substituted numbers before rearranging the equation (e.g., write '230 x 0.15 = V_s x 2.3' first). Examiners award marks for this substitution step even if you make a calculation error later.
3
If a 6-mark or short-answer question asks you to 'explain' the equation V_p x I_p = V_s x I_s, you must state two things to get full marks: the transformer is 100% efficient AND this relies on the conservation of energy.
4
Pay attention to units! If a question gives you a value in kilovolts (kV) or milliamps (mA), you must convert it to Volts (V) or Amps (A) before substituting into the equation.

Key Terms(9)

Ideal transformer: A theoretical transformer that operates at exactly 100% efficiency, meaning no energy is lost as heat to the surroundings or the iron core.
100% efficiency: A state where the total power input to a device is exactly equal to its useful power output, with no wasted energy.
Conservation of Energy: The fundamental physics principle stating that energy cannot be created or destroyed, only transferred or stored.
Power: The rate at which energy is transferred, measured in Watts (W).
Potential difference: The energy transferred per unit charge passing between two points in a circuit, measured in Volts (V).
Current: The rate of flow of electrical charge in a circuit, measured in Amps (A).
Primary coil: The wire coil in a transformer that is connected to the input alternating current supply.
Secondary coil: The output wire coil in a transformer where the new potential difference is induced.
Alternating current (AC): An electric current that repeatedly reverses its direction of flow, required for a transformer to work.

Previous Subtopic: Step-up and Step-down TransformersStep-up and Step-down Transformers Next Subtopic: High Voltage Transmission AdvantagesHigh Voltage Transmission Advantages

Back to Transformer Power Equation

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Key Terms(9)

Ideal transformer: A theoretical transformer that operates at exactly 100% efficiency, meaning no energy is lost as heat to the surroundings or the iron core.
100% efficiency: A state where the total power input to a device is exactly equal to its useful power output, with no wasted energy.
Conservation of Energy: The fundamental physics principle stating that energy cannot be created or destroyed, only transferred or stored.
Power: The rate at which energy is transferred, measured in Watts (W).
Potential difference: The energy transferred per unit charge passing between two points in a circuit, measured in Volts (V).
Current: The rate of flow of electrical charge in a circuit, measured in Amps (A).
Primary coil: The wire coil in a transformer that is connected to the input alternating current supply.
Secondary coil: The output wire coil in a transformer where the new potential difference is induced.
Alternating current (AC): An electric current that repeatedly reverses its direction of flow, required for a transformer to work.

Transformer Power Equation

The Principle of an Ideal Transformer

Think about the plug heating up when you charge your phone—that wasted heat means real chargers are not perfectly efficient.
However, in physics, we often start by assuming an ideal transformer where absolutely no energy is lost to the iron core or surroundings as heat.
This theoretical model operates at 100% efficiency, meaning the exact amount of power entering the device is equal to the power leaving it.
This concept relies entirely on the fundamental Law of Conservation of Energy, which states that energy cannot be created or destroyed.

The Power Equation

We can express this conservation of energy mathematically. Electrical power ( $P$ ) is the rate of energy transfer, calculated by multiplying the potential difference ( $V$ ) by the current ( $I$ ).
Because the power entering the primary coil must equal the power leaving the secondary coil, we can state that Power in = Power out.

V_p \times I_p = V_s \times I_s

Where:

$V_p$ = potential difference across the primary coil (in Volts, V)
$I_p$ = current in the primary coil (in Amps, A)
$V_s$ = potential difference across the secondary coil (in Volts, V)
$I_s$ = current in the secondary coil (in Amps, A)

The Inverse Relationship

Because the total power remains constant across a 100% efficient transformer, potential difference and current must be inversely proportional.
In a step-up transformer, the potential difference increases ( $V_s > V_p$ ), so the current must decrease proportionally ( $I_s < I_p$ ).
In a step-down transformer, the potential difference decreases ( $V_s < V_p$ ), so the current must increase ( $I_s > I_p$ ).
This inverse relationship is exactly why the National Grid transmits electricity at extremely high potential differences. Stepping up the potential difference means a much lower current, which drastically reduces the amount of energy wasted as heat in transmission wires.
Note that this process only works because transformers are supplied with an alternating current (AC), which creates the changing magnetic field needed to induce a potential difference.

Worked Example: Calculating Current

Step 1: State the formula and identify the known values.

$V_p \times I_p = V_s \times I_s$
$V_p = 20,000\text{ V}$ , $V_s = 400,000\text{ V}$ , $I_p = 5,000\text{ A}$

Step 2: Substitute the values into the equation.

$20,000 \times 5,000 = 400,000 \times I_s$

Step 3: Rearrange to solve for $I_s$ .

$100,000,000 = 400,000 \times I_s$
$I_s = \frac{100,000,000}{400,000}$

Step 4: Calculate the final answer with units.

$I_s = 250\text{ A}$

Worked Example: Calculating Potential Difference

Step 1: State the formula and identify the known values.

$V_p \times I_p = V_s \times I_s$
$V_p = 230\text{ V}$ , $I_p = 0.15\text{ A}$ , $I_s = 2.3\text{ A}$

Step 2: Substitute the values into the equation.

$230 \times 0.15 = V_s \times 2.3$

Step 3: Rearrange to solve for $V_s$ .

$34.5 = V_s \times 2.3$
$V_s = \frac{34.5}{2.3}$

Step 4: Calculate the final answer with units.

$V_s = 15\text{ V}$

Sign up to continue reading

Get full access to revision notes, key terms, and exam tips for every subtopic.

Exam Tips

Common Mistake
Students often use the word 'voltage' in their written answers, but Edexcel explicitly prefers and awards marks for the term 'potential difference'.
2
In calculation questions, always write down your substituted numbers before rearranging the equation (e.g., write '230 x 0.15 = V_s x 2.3' first). Examiners award marks for this substitution step even if you make a calculation error later.
3
If a 6-mark or short-answer question asks you to 'explain' the equation V_p x I_p = V_s x I_s, you must state two things to get full marks: the transformer is 100% efficient AND this relies on the conservation of energy.
4
Pay attention to units! If a question gives you a value in kilovolts (kV) or milliamps (mA), you must convert it to Volts (V) or Amps (A) before substituting into the equation.

Key Terms(9)

Ideal transformer: A theoretical transformer that operates at exactly 100% efficiency, meaning no energy is lost as heat to the surroundings or the iron core.
100% efficiency: A state where the total power input to a device is exactly equal to its useful power output, with no wasted energy.
Conservation of Energy: The fundamental physics principle stating that energy cannot be created or destroyed, only transferred or stored.
Power: The rate at which energy is transferred, measured in Watts (W).
Potential difference: The energy transferred per unit charge passing between two points in a circuit, measured in Volts (V).
Current: The rate of flow of electrical charge in a circuit, measured in Amps (A).
Primary coil: The wire coil in a transformer that is connected to the input alternating current supply.
Secondary coil: The output wire coil in a transformer where the new potential difference is induced.
Alternating current (AC): An electric current that repeatedly reverses its direction of flow, required for a transformer to work.

Previous Subtopic: Step-up and Step-down TransformersStep-up and Step-down Transformers Next Subtopic: High Voltage Transmission AdvantagesHigh Voltage Transmission Advantages

Back to Transformer Power Equation

Put your knowledge into practice — try past paper questions for Physics

Key Terms(9)

Ideal transformer: A theoretical transformer that operates at exactly 100% efficiency, meaning no energy is lost as heat to the surroundings or the iron core.
100% efficiency: A state where the total power input to a device is exactly equal to its useful power output, with no wasted energy.
Conservation of Energy: The fundamental physics principle stating that energy cannot be created or destroyed, only transferred or stored.
Power: The rate at which energy is transferred, measured in Watts (W).
Potential difference: The energy transferred per unit charge passing between two points in a circuit, measured in Volts (V).
Current: The rate of flow of electrical charge in a circuit, measured in Amps (A).
Primary coil: The wire coil in a transformer that is connected to the input alternating current supply.
Secondary coil: The output wire coil in a transformer where the new potential difference is induced.
Alternating current (AC): An electric current that repeatedly reverses its direction of flow, required for a transformer to work.