Question

The three resistances of equal value are arranged in the different combinations shown below. Arrange them in increasing order of power dissipation

• A. III < II < IV < I
• B. II < III < IV < I
• C. I < IV < III < II
• D. I < III < II < IV

Answer 1

Answer: (A)

Let each resistance $=R$
For I: $P_{1}=i^{2} R_{e q}=i^{2}(R+R+R)=i^{2}(3 R)$
For II: $P_{2}=i^{2} R_{e q}=i^{2} \times \frac{R(R+R)}{R+(R+R)}=i^{2}(2 R / 3)$
For III: $P_{3}=i^{2} R_{e q}=i^{2}(R / 3)$
For IV: $P_{4}=i^{2} R_{e q}=i^{2} \times(R / 2+R)=i^{2}(3 R / 2)$
Thus, $P _{3}< P _{2}< P _{4}< P _{1}$