Transformer Physics Example 4

Follow the full solution, then compare it with the other examples linked below.

hard

A transformer with

90\%

efficiency steps up

240 \text{ V}

12{,}000 \text{ V}

. If the secondary delivers

2 \text{ A}

, what is the primary current and the power wasted as heat?

1
Output power: $P_{\text{out}} = V_s I_s = 12{,}000 \times 2 = 24{,}000 \text{ W}$ .
2
Input power: $P_{\text{in}} = \frac{P_{\text{out}}}{\eta} = \frac{24{,}000}{0.9} \approx 26{,}667 \text{ W}$ .
3
Primary current: $I_p = \frac{P_{\text{in}}}{V_p} = \frac{26{,}667}{240} \approx 111 \text{ A}$ . Power wasted: $P_{\text{waste}} = P_{\text{in}} - P_{\text{out}} = 26{,}667 - 24{,}000 = 2{,}667 \text{ W}$ .

Answer

I_p \approx 111 \text{ A}, \quad P_{\text{waste}} \approx 2.67 \text{ kW}

Real transformers lose some energy to heat through resistance in the coils and eddy currents in the core. Efficiency is always less than

100\%

, requiring more input power than the useful output.

About Transformer

A device that changes AC voltage using electromagnetic induction between two coils on a shared iron core.

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