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Q.
A transformer connected to $220\, V$ mains is used to light a lamp of rating $100\, W$ and $110\, V$. If the primary current is $0.5\, A$, the efficiency of the transformer is (approximately)
Key Concept Efficiency is defined as the ratio of output power and input power.
i.e. $\eta \%=\frac{p_{ out }}{p_{ in }} \times 100$
For an ideal transformer, $p_{\text {out }}=p_{\text {in }}$ so, $\eta=100 \%$ but in practical, efficiency of transformer lies between $70-90 \%$.
Given, $V=200\, V , I_{p}=0.5\, A ,\, P_{s}=100\, W$
We know that, $P_{p}=V_{p} \cdot I_{P}=220 \times 0.5$
$P_{p}=110\, W$
$\eta=\frac{P_{S}}{P_{p}}$
Efficiency of the transformer,
$=\frac{100}{110}=0.9 \text { or } 90 \%$