Question

The equivalent resistance of 5 equal resistances connected in series and parallel are \( R_1 \) and \( R_2 \) respectively. If \( R_1 = nR_2 \), then what will be the possible value of \( n \)?

• A. \( \frac{1}{25} \)
• B. \( \frac{1}{5} \)
• C. \( 5 \)
• D. \( 25 \)

Hint:

For resistors in series, simply add their resistances; for parallel resistors, sum their reciprocals and take the inverse.

Answer 1

The Correct Option is D

Step 1: Equivalent resistance for resistors in series: \[ R_1 = 5R \] Step 2: Equivalent resistance for resistors in parallel: \[ \frac{1}{R_2} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + \frac{1}{R} \] \[ R_2 = \frac{R}{5} \] Step 3: Given \( R_1 = nR_2 \): \[ 5R = n \cdot \frac{R}{5} \] \[ n = 25 \] \[ \therefore \text{The correct answer is } 25. \] \[ \boxed{25} \]