Question

By what percentage will the illumination of the lamp decrease if the current drops by 20%?

• A. \(46\%\)
• B. \(26\%\)
• C. \(36\%\)
• D. \(56\%\)

Answer 1

The Correct Option is C

To determine the percentage decrease in a lamp's illumination when the current drops by 20%, we utilize the principle that illumination is directly proportional to the square of the current, derived from the power formula \(P \propto I^2\). Here, \(P\) signifies power and \(I\) represents current. This relationship allows us to calculate the change in illumination.

1. Initial illumination is proportional to the square of the original current, \(I^2\).
2. A 20% reduction in current results in a new current of \(I_{\text{new}} = I - 0.2I = 0.8I\).
3. The new illumination is proportional to \((0.8I)^2 = 0.64I^2\).
4. The percentage decrease in illumination is calculated as:

\(\text{Percentage Decrease} = \left(\frac{I^2 - 0.64I^2}{I^2}\right) \times 100\% = (1 - 0.64) \times 100\% = 0.36 \times 100\% = 36\%\)

Consequently, the lamp's illumination experiences a 36% reduction.

The correct answer is \(36\%\).