Transformer calculations always come back to three equations

Transformers — AQA A-Level Physics

Every transformer question you will see in an exam can be solved using some combination of three relationships. Knowing when to use each one is the skill.

The three core equations

\frac{V_s}{V_p} = \frac{N_s}{N_p}

$V_s$: secondary voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference. (V)
$V_p$: primary voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference. (V)
$N_s$: secondary turns
$N_p$: primary turns

$$V_p I_p = V_s I_s$$

$V_p I_p$: input powerThe rate of energy transfer. Measured in watts (W). (W)
$V_s I_s$: output powerThe rate of energy transfer. Measured in watts (W). (W)

\text{EfficiencyThe ratio of useful energyThe capacity to do work. Measured in joules (J). output to total energy input, expressed as a fraction or percentage.} = \frac{V_s I_s}{V_p I_p} \times 100\%

$V_s I_s$: output powerThe rate of energy transfer. Measured in watts (W). (W)
$V_p I_p$: input power (W)

If the question says 'ideal transformer' or 'assume no energy losses', use $VpIp = VsIs directly$.
If the question gives an efficiencyThe ratio of useful energy output to total energy input, expressed as a fraction or percentage. (e.g. 95%), then output $power = 0.95 x$ input power. Replace $VsIs = VpIp$ with $VsIs = 0.95 x VpIp$.
If the question mentions the National Grid or cable resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to currentThe rate of flow of charge. Measured in amperes (A).. Measured in ohms (Ω)., you also need $P_{\text{loss}} = I^{2} R$.
Many 4-5 mark questions chain two of these together. For example: use the turns ratio to find Vs, then use power conservation to find Is.

Common Mistake MEDIUM

Students often: Using $VpIp = VsIs$ when the question states the transformer is not ideal or gives an efficiency.
Instead: $VpIp = VsIs$ only holds for a 100% efficient (ideal) transformer. If efficiency is given, use $VsIs = eta x VpIp. Forgetting this will give a secondary current$ that is too high.