Question

In a resistor network with resistance \( R \), what is the ratio of the total resistance when the resistances are combined in series and parallel?

• A. \( 1 : \frac{2}{\sqrt{2}} \)
• B. 1 : 9
• C. 81 : 1
• D. \( 27 : 1 \)

Hint:

In series circuits, resistances add up, whereas in parallel circuits, the total resistance decreases and can be found by the reciprocal formula.

Answer 1

The Correct Option is D

Step 1: Series and parallel combination of resistors.
When resistors are combined in series, the total resistance is the sum of the individual resistances: \[ R_{\text{total}} = R_1 + R_2 + \dots \] In parallel, the total resistance is given by: \[ \frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots \]
Step 2: Conclusion.
The ratio of the total resistances for series and parallel combinations will be \( 27 : 1 \), making option (D) the correct answer.