Question

The sum of two resistors is 6Ω and their equivalent resistance when connected in parallel is 1.5Ω. The product of the two resistances is

• A. 4Ω
• B. 9Ω
• C. 7.5Ω
• D. 4.3Ω

Answer 1

The Correct Option is B

Let the two resistances be \( R_1 \) and \( R_2 \). Given: \( R_1 + R_2 = 6 \) Ω — (1) When connected in parallel, the equivalent resistance is: \[ \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} = \frac{R_1 + R_2}{R_1 R_2} \] Substitute values: \[ \frac{1}{1.5} = \frac{6}{R_1 R_2} \Rightarrow R_1 R_2 = 1.5 \times 6 = 9 \]

The correct option is (B): \(9Ω\)