Answer:
The ratio is 0.667.
Explanation:
We are given two incandescent lights which have ratings of 75 W and 50 W .
Both bulbs operate at the same voltage.
The equation of power consumed is given by P = [tex]\frac{V^2}{R}[/tex]
Therefore the resistance for the 75 W bulb = [tex]\frac{V^2}{75}[/tex]
Therefore the resistance for the 50 W bulb = [tex]\frac{V^2}{50}[/tex]
Therefore the ratio of the resistance for the 75 W bulb to the resistance of the 50 W bulb is equal to
= [tex]\frac{\frac{V^2}{75} }{\frac{V^2}{50} }[/tex] = [tex]\frac{V^2}{75} \times \frac{50}{V^{2} } = \frac{50}{75} = \frac{2}{3}[/tex] = 0.667.
The ratio is 0.667.
According to the question,
Rating of two incandescent lights,
Power consumed,
Now the resistance,
When P = 75 W,
→ [tex]R = \frac{V^2}{75}[/tex]
When P = 50 W,
→ [tex]R = \frac{V^2}{50}[/tex]
hence,
The ratio of resistance will be:
= [tex]\frac{\frac{V^2}{75} }{\frac{V^2}{50} }[/tex]
= [tex]\frac{V^2}{75}\times \frac{50}{V^2}[/tex]
= [tex]\frac{50}{75}[/tex]
= [tex]0.667[/tex]
Thus the answer above is right.
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