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When the current flowing through a lamp is decreased by 2%, then the percentage change in the power consumed by the lamp will be Only one correct answerA.5.48%B.4.25%C.3.96%D.6.75%

Question

When the current flowing through a lamp is decreased by 2%, then the percentage change in the power consumed by the lamp will be Only one correct answerA.5.48%B.4.25%C.3.96%D.6.75%

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Solution

The power P in an electrical circuit is given by the formula P = I^2R, where I is the current and R is the resistance.

If the current I is decreased by 2%, the new current I' is I' = I - 0.02I = 0.98I.

The new power P' is then given by P' = (0.98I)^2R = 0.9604I^2R.

The percentage change in power is then given by (P' - P) / P * 100%.

Substituting P' = 0.9604I^2R and P = I^2R gives ((0.9604I^2R - I^2R) / I^2R) * 100% = (0.9604 - 1) * 100% = -3.96%.

Therefore, the power consumed by the lamp decreases by 3.96% when the current is decreased by 2%. So, the correct answer is C. 3.96%.

This problem has been solved

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