Question

A transformer is used to light a $140\text{W},24\text{V}$ lamp from $240\text{V}$ AC mains. The current in mains cable is $0.7\text{A}$, find the efficiency (approximate value) of transformer.

• A. $50\%$
• B. $76\%$
• C. $83\%$
• D. $91\%$

Answer 1

The correct option is C $83\%$

Resistance of the lamp,

$R=\frac{E_S^2}{P}=\frac{{24}^2}{140}\approx 4.11\Omega$

Current in secondary coil is,

$i_S=\frac{E_S}{R}=\frac{24}{4.11}=5.84\text{A}$

Power at primary coil is,

$P_{\text{input}}=E_P{i}_P=240\times 0.7=168\text{W}$

Power at secondary coil is,

$P_{\text{output}}=E_S{i}_S=24\times 5.84=140.16\text{W}$

Now, efficiency of the transformer is,

$\eta =\frac{P_{\text{output}}}{P_{\text{input}}}\times 100$

$\Rightarrow \eta =\frac{140.16}{168}\times 100\approx 83\%$

Hence, option $\left(C\right)$ is the correct answer.