Question

A transformer is used to light 100 W – 110V lamp from 220V mains. If the main current is 0.5A, the efficiency of the transformer is –
A) 90$\%$
B) 95$\%$
C) 96$\%$
D) 99$\%$

Answer 1

We need to find the relation between the power rating of a device, its operating voltage and the input voltage and the power from the supply to find the efficiency of the transformer which converts the given input voltage to the required value.

Complete Solution :
We are given a transformer which is used in a device to down the input voltage from 220V to the operating voltage of the device, i.e., 110V. We are also given the power consumed by the device, which can be regarded as the output voltage of the whole setup.
Now, we know that the power supplied to the transformer and the power from the secondary coil will be the same. The power can be defined as the product of the voltage and the current. So, we can find the power in the input as –

& P=VI \\\ & \Rightarrow {{P}_{i}}=220\times 0.5A \\\ & \therefore {{P}_{i}}=110W \\\ \end{aligned}$$ Now, we can find the output current by equating the powers as – $$\begin{aligned} & {{P}_{i}}={{P}_{f}} \\\ & \Rightarrow 110W={{V}_{o}}{{I}_{o}} \\\ & \Rightarrow {{I}_{o}}=\dfrac{110V}{110W} \\\ & \therefore {{I}_{o}}=1A \\\ \end{aligned}$$ Now, using this we can find the output power as – $$\begin{aligned} & {{P}_{o}}={{V}_{o}}{{I}_{o}} \\\ & \Rightarrow {{P}_{o}}=110\times 1 \\\ & \therefore {{P}_{o}}=110W \\\ \end{aligned}$$ Now, we can find the ratio of the power consumed by the device to the power given to the device from the transformer. This ratio will give the efficiency of the transformer which can be multiplied by 100 to get the required percentage efficiency as – $$\begin{aligned} & \text{efficiency, }\eta \text{=}\dfrac{{{P}_{device}}}{{{P}_{o}}}\times 100 \\\ & \Rightarrow \eta =\dfrac{100W}{110W}\times 100 \\\ & \therefore \eta =90.90\% \\\ \end{aligned}$$ The efficiency of the transformer is therefore given approximately equal to 90$$\%$$. **Hence, the correct answer is option A.** **Note:** We need not find the current that the transformer gives as output while stepping down from the mains voltage to the required voltage. We can directly use the input power as the power that is given to the device as there is no transformer loss given here.