Find the current and resistance drawn by a bulb rated 40 𝑊; 220 𝑉, when it is connected to a 220 𝑉 supply. If the given bulb is replaced by a bulb if rating 25 𝑊; 220 𝑉, will there be any change in the value of current and resistance? Justify your answer and determine the change.

Case 1: power of bulb, P = 40 watt 

The voltage supplied across the bulb, 𝑉 = 220𝑉 

We know, power supplied by bulb, 𝑃 = 𝑉𝐼

or, 40 = 220 × 𝐼

$\Rightarrow$Current 𝐼 = 40/220 = 2/11 = 0. 18 𝐴𝑚𝑝 

Again, using the formula, 𝑃 = 𝑉²/𝑅 to find resistance of bulb

or, 𝑅 = 𝑉²/𝑃 

$\Rightarrow$𝑅 = (220)²/40 = 48400/40 = 1210 𝑜ℎ𝑚

Case 2: if the given bulb is replaced by a bulb operating 25 𝑊; 220 V

Current, 𝐼' = 𝑃'/𝑉 = 25/220 = 0. 1136 𝐴𝑚𝑝 

resistance, 𝑅' = 𝑉²/𝑃' = (220)²/25 = 1936 𝑜ℎ𝑚. 

When we change the bulb, current and resistance will be changed. 

Change in current = 𝐼 − 𝐼' = 0. 18 − 0. 1136 = 0. 0664 𝐴𝑚𝑝 

The current decreases when we use 25 watt bulb in place of 40 watt bulb. 

Change in resistance = 1936 − 1210 = 726 𝑜ℎ𝑚

 The resistance increase when we use 25 watt bulb in place of 40 watt.