Two Bulbs Are Rated (P1, V) and (P2, V). If They Are Connected (I) in Series and (Ii) in Parallel Across a Supply V, Find the Power Dissipated in the Two Combinations in Terms of P1 and P2. - Physics

Question

Two bulbs are rated (P1, V) and (P2, V). If they are connected (i) in series and (ii) in parallel across a supply V, find the power dissipated in the two combinations in terms of P1 and P2.

Solution

Given Bulbs are rated as (P1, V) and (P2, V) respectively
The resistance of 1st bulbs R_1 = V^2/P_1

The resistance of 2nd bulbs R_2 = V^2/P_2

(i) When both are connected in series with a power supply of voltage V.  As both the bulbs are in series connection hence both will have the same amount of current flowing through them.

i = V/(R_1 + R_2) = V/(V^2/P_1 + V^2/P_2) = 1/V((P_1P_2)/(P_1 + P_2))

Power dissipated in the circuit

P_d = i^2(R_1 + R_2) = 1/V^2((P_1P_2)/(P_1 + P_2))^2(V^2/P_1 + V^2/P_2)

P_d = (P_1P_2)/(P_1 + P_2)

(ii) When both are connected in parallel  In this case, both bulbs will get the same voltage supply. Hence, power dissipated

P_d = V^2/R_1 + V^2/R_2 = V^2(P_1/V^2 + P_2/V^2)

P_d = P_1 + P_2.

Concept: Cells in Series and in Parallel
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