Answer :
Answer:
To find the highest and lowest resistance that can be made by joining five 10 ohms resistors, we can use the series and parallel combination of resistors.
1. **Highest Resistance (Series Combination)**:
When resistors are connected in series, the total resistance is the sum of individual resistances.
\[ R_{\text{total}} = R_1 + R_2 + R_3 + R_4 + R_5 \]
\[ R_{\text{highest}} = 10 \, \Omega + 10 \, \Omega + 10 \, \Omega + 10 \, \Omega + 10 \, \Omega = 50 \, \Omega \]
2. **Lowest Resistance (Parallel Combination)**:
When resistors are connected in parallel, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances.
\[ \frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4} + \frac{1}{R_5} \]
\[ \frac{1}{R_{\text{lowest}}} = \frac{1}{10 \, \Omega} + \frac{1}{10 \, \Omega} + \frac{1}{10 \, \Omega} + \frac{1}{10 \, \Omega} + \frac{1}{10 \, \Omega} \]
\[ \frac{1}{R_{\text{lowest}}} = \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} = \frac{5}{10} \]
\[ \frac{1}{R_{\text{lowest}}} = \frac{5}{10} \]
\[ R_{\text{lowest}} = \frac{10}{5} = 2 \, \Omega \]
So, the highest resistance is 50 ohms when the resistors are connected in series, and the lowest resistance is 2 ohms when the resistors are connected in parallel.
Circuit Diagrams:
1. Series Combination:
```
┌─[10Ω]───[10Ω]───[10Ω]───[10Ω]───[10Ω]─┐
└───────────────────────────────────────┘
```
2. Parallel Combination:
```
┌─[10Ω]─┐
├─[10Ω]─┤
├─[10Ω]─┤
├─[10Ω]─┤
└─[10Ω]─┘
```
Explanation:
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