Question

Three identical resistors are arranged three different ways as pictured in figure.
What is the correct ranking of these arrangements, according to their equivalent resistance values, greatest first?

• A. 1, 2, 3
• B. 1, 3, 2
• C. 2, 3, 1
• D. 2, 1, 3
• E. 3, 1, 2

Answer 1

Answer: (B)

1, 3, 2

Case 1 : Equivalent resistance of series combination $R_1=R+R+R=3R$

Case 2 : Equivalent resistance of parallel combination $\frac{1}{R_2}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}$

$⟹$ $R_2=\frac{R}{3}$

Case 3 : Equivalent resistance of resistors connected in parallel $R^{\prime }=\frac{R\times R}{R+R}=\frac{R}{2}$

$\therefore$ Equivalent resistance of mixed combination $R_3=R+\frac{R}{2}=1.5R$

$⟹$ $R_1>R_3>R_2$

Hence option B is correct.