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Transformer Calculations (Oxford AQA IGCSE Physics)

Revision Note

Dan Mitchell-Garnett

Written by: Dan Mitchell-Garnett

Reviewed by: Caroline Carroll

Transformer Calculations

  • The output potential difference across the secondary coil of a transformer depends on:

    • The number of turns on the primary and secondary coils

    • The input potential difference across the primary coil

The transformer equation

  • The transformer equation can be used to calculate the potential difference across each coil:

V subscript p over V subscript s space equals space n subscript p over n subscript s

  • Where:

    • Vp = potential difference across the primary coil measured in volts (V)

    • Vs = potential difference across the secondary coil measured in volts (V)

    • np = number of turns in the primary coil

    • ns = number of turns in the secondary coil

  • The equation above can be flipped upside down to give:

V subscript s over V subscript p space equals space n subscript s over n subscript p

  • The equations above show that:

    • The ratio of the potential differences across the primary and secondary coils of a transformer is equal to the ratio of the number of turns on each coil

Step-up transformer

  • A step-up transformer increases the potential difference of a power source

  • A step-up transformer has more turns on the secondary coil than on the primary coil (ns > np)

    • The number of turns increases from primary to secondary

    • So the potential difference increases from primary to secondary

Step-down transformer

  • A step-down transformer decreases the potential difference of a power source

  • A step-down transformer has fewer turns on the secondary coil than on the primary coil (ns < np)

    • The number of turns decreases from primary to secondary

    • So the potential difference decreases from primary to secondary

Worked Example

A transformer has 20 turns on the primary coil and 800 turns on the secondary coil. The input potential difference across the primary coil is 500 V.

(a) Calculate the output potential difference

(b) State what type of transformer this is

Answer:

Part a)

Step 1: List the known quantities

  • Number of turns in the primary coil, np = 20

  • Number of turns in the secondary coil, ns = 800

  • Potential difference across the primary coil, Vp = 500 V

Step 2: Write the transformer equation from the equation sheet

  • The transformer equation on the equation sheet is given as

V subscript p over V subscript s space equals space n subscript p over n subscript s

  • Flipping this equation with the secondary coil's variables on the top will make rearranging this equation much easier

V subscript s over V subscript p space equals space n subscript s over n subscript p

Step 3: Rearrange for Vs

  • The equation with secondary potential difference as the subject is:

V subscript s space equals space V subscript p space cross times space n subscript s over n subscript p

Step 4: Substitute the known quantities

V subscript s space equals space 500 space cross times space 800 over 20

V subscript s space equals space 20 space 000 space straight V

Part b)

Step 1: Determine if the potential difference has increased or decreased

  • The potential difference across the primary coil is 500 V

  • The potential difference in the secondary coil is 20 000 V

  • Therefore, the potential difference has increased from primary to secondary

Step 2: State whether the transformer is step-up or step-down

  • The potential difference has increased

  • So this is a step-up transformer

Examiner Tips and Tricks

When you are using the transformer equation, there will be less rearranging to do in a calculation if the variable which you are trying to find is on the numerator (top line) of the fraction.

The Ideal Transformer Equation

  • An ideal transformer would be 100% efficient

    • Although transformers can increase the voltage of a power source, due to the law of conservation of energy, they cannot increase the power output

  • If a transformer is 100% efficient:

input space power space equals space output space power

  • The equation to calculate electrical power is:

P space equals space I space cross times space V

  • Where:

    • P = power in watts (W)

    • V = potential difference in volts (V)

    • I = current in amps (A)

  • Therefore, if a transformer is 100% efficient then:

I subscript p space cross times space V subscript p space equals space I subscript s space cross times space V subscript s

  • Where:

    • Vp = potential difference across primary coil in volts (V)

    • Ip = current through primary coil in Amps (A)

    • Vs = potential difference across secondary coil in volts (V)

    • Is = current through secondary coil in Amps (A)

  • The equation above could also be written as:

P subscript s space equals space I subscript p space cross times space V subscript p

  • Where:

    • Ps = output power (power produced in secondary coil) in watts (W)

Worked Example

A transformer in a travel adapter steps up a 115 V ac mains electricity supply to the 230 V needed for the hair dryer. A current of 5 A flows through the hairdryer.

Assuming that the transformer is 100% efficient, calculate the current drawn from the mains supply. 

Answer:

Step 1: List the known quantities

  • Voltage in primary coil, Vp = 115 V

  • Voltage in secondary coil, Vs = 230 V

  • Current in secondary coil, Is = 5 A

Step 2: Write the equation linking the known values to the current from the supply, Ip

I subscript p space cross times space V subscript p space equals space I subscript s space cross times space V subscript s

Step 3: Rearrange the equation to make Ip the subject

I subscript p space equals space fraction numerator I subscript s space cross times space V subscript s over denominator V subscript p end fraction

Step 4: Substitute int he known values to calculate

I subscript p space equals space fraction numerator 5 space cross times space 230 over denominator 115 end fraction

Step 5: Calculate a value for Ip and include the correct unit

I subscript p space equals space 10 space straight A

Turn Ratio

  • It is the ratio of turns on the primary coil to turns on the secondary coil that determine the change in potential difference

    • This can be shown by the transformer equation

V subscript p over V subscript s space equals space n subscript p over n subscript s

  • The right-hand side of the equation is the turn ratio

    • The change in potential difference in the transformer can be determined without knowing the number of turns in each coil, as long as the ratio of turns is known

    • If the ratio is increased, the change in potential difference is also increased by the same factor

  • The turns ratio is selected to produce the required output potential difference from a given input potential difference

Worked Example

A step-down transformer is connected to a supply of 0.16 kV. The primary coil has 32× more turns than the secondary coil.

Calculate the output potential difference.

Answer:

Step 1: List the known quantities

  • Potential difference across the primary coil, Vp = 0.16 kV

  • Number of turns on primary coil = np

  • Number of turns on secondary coil = ns

Step 2: Convert kV into V

  • There are 1000 V in 1 kV

V subscript p space equals space 0.16 space cross times space 1000 space equals space 160 space straight V

Step 3: Write an expression relating the numbers of turns

  • There are 32 times more turns on the primary coil than on the secondary coil

n subscript p space equals space 32 n subscript s

Step 4: Write down the transformer equation

  • From the equation sheet:

V subscript p over V subscript s space equals space n subscript p over n subscript s

  • Flip the equation to find secondary potential difference

V subscript s over V subscript p space equals space n subscript s over n subscript p

Step 5: Substitute in the expression relating number of turns

n subscript p over n subscript s space equals space 32

V subscript p over V subscript s space equals space n subscript p over n subscript s space equals space 32

Step 6: Rearrange for potential difference across the secondary coil

V subscript p over V subscript s space equals space 32

V subscript s space equals space V subscript p over 32

Step 7: Substitute in the potential difference across the primary coil

V subscript s space equals space 160 over 32

V subscript s space equals space 5.0 space straight V

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    Author
    Reviewer
    Dan Mitchell-Garnett

    Author: Dan Mitchell-Garnett

    Expertise: Physics Content Creator

    Dan graduated with a First-class Masters degree in Physics at Durham University, specialising in cell membrane biophysics. After being awarded an Institute of Physics Teacher Training Scholarship, Dan taught physics in secondary schools in the North of England before moving to Save My Exams. Here, he carries on his passion for writing challenging physics questions and helping young people learn to love physics.

    Caroline Carroll

    Author: Caroline Carroll

    Expertise: Physics Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.