You are supplied with a number of `100Omega` resistors. How could you combine some of these resistors to make a `250 Omega` resistor?

Answer

To create a `250 Ω` resistor using `100 Ω` resistors, we can follow these steps:

### Step 1: Connect Two Resistors in Series
First, take two `100 Ω` resistors and connect them in series. The total resistance of resistors in series is simply the sum of their resistances.

\[ R_{series} = R_1 + R_2 = 100 Ω + 100 Ω = 200 Ω \]

### Step 2: Connect Two Resistors in Parallel
Next, take another two `100 Ω` resistors and connect them in parallel. The formula for the equivalent resistance \( R_{parallel} \) of two resistors in parallel is given by:

\[ \frac{1}{R_{parallel}} = \frac{1}{R_1} + \frac{1}{R_2} \]

Substituting the values:

\[ \frac{1}{R_{parallel}} = \frac{1}{100 Ω} + \frac{1}{100 Ω} = \frac{2}{100 Ω} \]

Now, solving for \( R_{parallel} \):

\[ R_{parallel} = \frac{100 Ω}{2} = 50 Ω \]

### Step 3: Combine the Two Sets in Series
Now, take the equivalent resistance from the first step (200 Ω) and the equivalent resistance from the second step (50 Ω) and connect them in series:

\[ R_{total} = R_{series} + R_{parallel} = 200 Ω + 50 Ω = 250 Ω \]

### Conclusion
Thus, by connecting two `100 Ω` resistors in series to get `200 Ω` and two `100 Ω` resistors in parallel to get `50 Ω`, and then combining these two results in series, we achieve a total resistance of `250 Ω`.

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