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Question 13

Different combination of 3 resistors of equal resistance $$R$$ are shown in the figures. The increasing order for power dissipation is:
(A)

image

(B)

image

(C)

image

(D)

image

$$P = I^2 R_{eq}$$

Therefore, the increasing order of power dissipation will be identical to the increasing order of equivalent resistance ($$R_{eq}$$).

Circuit A:  $$R_{parallel} = \frac{R}{2}$$

$$R_{eq, A} = \frac{R}{2} + R = \mathbf{1.5R}$$

Circuit B: $$R_{series} = 2R$$

$$R_{eq, B} = \frac{2R \times R}{2R + R} = \frac{2}{3}R \approx \mathbf{0.67R}$$

Circuit C: $$R_{eq, C} = \frac{R}{3} \approx \mathbf{0.33R}$$

Circuit D: $$R_{eq, D} = R + R + R = \mathbf{3R}$$

$$0.33R < 0.67R < 1.5R < 3R$$

$$\implies R_{eq, C} < R_{eq, B} < R_{eq, A} < R_{eq, D}$$

$$\mathbf{P_C < P_B < P_A < P_D}$$

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