Question

10 resistors each of resistance 10Ω can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be_______ .

Answer 1

Correct Answer: 100

Step 1: Calculate \( R_{\text{max}} \) for Resistors in Series

When all 10 resistors (\( R \)) are connected in series, the maximum resistance is:

\[ R_{\text{max}} = 10R = 10 \times 10 = 100 \, \Omega \]

Step 2: Calculate \( R_{\text{min}} \) for Resistors in Parallel

When all 10 resistors (\( R \)) are connected in parallel, the minimum resistance is:

\[ R_{\text{min}} = \frac{R}{10} = \frac{10}{10} = 1 \, \Omega \]

Step 3: Find the Ratio \( \frac{R_{\text{max}}}{R_{\text{min}}} \)

The ratio is given by:

\[ \frac{R_{\text{max}}}{R_{\text{min}}} = \frac{100}{1} = 100 \]

Step 4: Verify \( R_{\text{min}} \)

From the above calculations:

\[ R_{\text{min}} = 1 \, \Omega \]

Final Answer:

• \( R_{\text{max}} = 100 \, \Omega \)
• \( R_{\text{min}} = 1 \, \Omega \)
• \( \frac{R_{\text{max}}}{R_{\text{min}}} = 100 \)