Question 5 – Rankers Physics

Power of Electrical Circuit: Practice Problem & Solution

Assertion (A): The rate at which energy is being delivered to a light bulb is lower after it has been on for a few seconds than just after it is turned on. Reason (R): As the filaments warms up, its resistance rises and the current falls.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Power of Electrical Circuit. Understanding the underlying formula is key to arriving at the correct answer below:

Concept: Resistance of metals increases with temperature. Power \(P = V^2/R\).
Formula: \(P = V^2/R\), \(R \propto T\).
Solution: As filament warms, its resistance \(R\) increases. For constant voltage \(V\), current \(I = V/R\) decreases, so power \(P = V^2/R\) delivered to the bulb also decreases. Thus, A and R are true and R explains A.

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