Question

What is the total resistance of two resistors, \( R \) and \( 2R \), when they are connected in parallel?

• A. \( \frac{R}{2} \)
• B. \( \frac{3R}{2} \)
• C. \( \frac{2R}{3} \)
• D. \( \frac{5R}{3} \)

Hint:

For resistors in parallel, the total resistance is always less than the smallest individual resistance.

Answer 1

The Correct Option is C

The formula for the total resistance \( R_t \) of two resistors, \( R_1 \) and \( R_2 \), connected in parallel is given by: \[ \frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} \] For the resistors \( R \) and \( 2R \), we have: \[ \frac{1}{R_t} = \frac{1}{R} + \frac{1}{2R} \] Simplifying: \[ \frac{1}{R_t} = \frac{2}{2R} + \frac{1}{2R} = \frac{3}{2R} \] Thus, \[ R_t = \frac{2R}{3} \]