The efffective resistance in series combination of two equal resistance is 's'. When they are joined in parallel the total resistance is p. If s = np then the maximum possible value of 'n' is

Options

A. 4
B. 1
C. 2
D. 3

Explanation

To solve the problem, we need to analyze the effective resistance in both series and parallel combinations of two equal resistances.

Let the resistance of each resistor be \( R \).

### Step 1: Calculate the effective resistance in series
When two resistors are connected in series, the effective resistance \( S \) is given by:
\[ S = R + R = 2R \]

### Step 2: Calculate the effective resistance in parallel
When the same two resistors are connected in parallel, the effective resistance \( P \) is given by:
\[ \frac{1}{P} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R} \]
This implies:
\[ P = \frac{R}{2} \]

### Step 3: Relate \( S \) and \( P \)
According to the problem, we have:
\[ S = nP \]
Substituting the expressions for \( S \) and \( P \):
\[ 2R = n \left( \frac{R}{2} \right) \]

### Step 4: Simplify the equation
To simplify, we can multiply both sides by 2 to eliminate the fraction:
\[ 4R = nR \]
Assuming \( R \neq 0 \), we can divide both sides by \( R \):
\[ 4 = n \]

### Conclusion
Thus, the maximum possible value of \( n \) is:
\[ \boxed{4} \]