A transformer is used to light a 100 W and 110 V lamp from a 220 V main. If the main current is 0.5 A, the eff

Question

A transformer is used to light a 100 W and 110 V lamp from a 220 V main. If the main current is 0.5 A, the efficiency of the transformer is approximately:

Accepted Answer

The efficiency ($\eta$) of a transformer is defined as the ratio of output power ($P_{out}$) to input power ($P_{in}$). 
1. **Output Power:** The lamp consumes 100 W. So, $P_{out} = 100$ W. 
2. **Input Power:** The power drawn from the mains is given by the product of the primary voltage ($V_p$) and the primary current ($I_p$). $P_{in} = V_p I_p = 220 	ext{ V} 	imes 0.5 	ext{ A} = 110$ W . 
3. **Efficiency:** $\eta = \frac{P_{out}}{P_{in}} 	imes 100\% = \frac{100}{110} 	imes 100\% \approx 90.9\%$. 
The closest approximation among the options is 90%.

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