Question

Two wires of resistances R and 2R are joined first in series and then in parallel. If the total resistances in the two conditions are \( R_1 \) and \( R_2 \) respectively, then \( R_1 / R_2 \) will be:

• A. 9
• B. \(\frac{1}{9}\)
• C. \(\frac{9}{2}\)
• D. \(\frac{2}{9}\)

Hint:

In a series circuit, total resistance is the sum of individual resistances. In parallel circuits, the reciprocal of total resistance is the sum of reciprocals of individual resistances.

Answer 1

The Correct Option is C

- For series connection: The total resistance is \[ R_1 = R + 2R = 3R \] - For parallel connection: The total resistance is \[ \frac{1}{R_2} = \frac{1}{R} + \frac{1}{2R} = \frac{2+1}{2R} = \frac{3}{2R} \] \[ R_2 = \frac{2R}{3} \] - Ratio of resistances: \[ \frac{R_1}{R_2} = \frac{3R}{\frac{2R}{3}} = \frac{3R \times 3}{2R} = \frac{9}{2} \]