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Question 25

A $$220$$ V, $$50$$ Hz AC source is connected to a $$25$$ V, $$5$$ W lamp and an additional resistance $$R$$ in series (as shown in figure) to run the lamp at its peak brightness, then the value of $$R$$ (in ohm) will be

Correct Answer: 975

Solution

Given:
Source: 220 V,50 Hz
Lamp: 25 V,5 W

Step 1: Current through lamp
For rated operation:

$$P=VI⇒5=25⋅I⇒I=\ \frac{\ 5}{25}=\ \frac{\ 1}{5}A\ \ $$

Step 2: Voltage across resistance R

$$V_R=220−25=195V$$

Step 3: Calculate R

$$V_R=IR\Rightarrow195=\frac{1}{5}R\ ⇒R=195\times5=975Ω$$

Final Answer:

975 Ω

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