Two resistances `R_(1) = 100 +- 3 Omega and R_(2) = 200 +- 4 Omega` are connected in series . Find the equivalent resistance of the series combination.

Options

A. `(66.7+-1.8)Omega`
B. `(66.7+-4.0)Omega`
C. `(66.7+-3.0)Omega`
D. `(66.7+-7.0)Omega`

Explanation

To find the equivalent resistance of two resistances connected in series, we follow these steps:

### Step 1: Understand the formula for equivalent resistance in series
In a series combination, the equivalent resistance \( R_{eq} \) is simply the sum of the individual resistances:
\[ R_{eq} = R_1 + R_2 \]

### Step 2: Identify the values of the resistances and their uncertainties
We have:
- \( R_1 = 100 \, \Omega \) with an uncertainty of \( \pm 3 \, \Omega \)
- \( R_2 = 200 \, \Omega \) with an uncertainty of \( \pm 4 \, \Omega \)

### Step 3: Substitute the values into the formula
Now we substitute the values into the formula for equivalent resistance:
\[ R_{eq} = (100 \, \Omega) + (200 \, \Omega) = 300 \, \Omega \]

### Step 4: Calculate the total uncertainty
When resistances are added, the uncertainties also add up. Therefore, we calculate the total uncertainty:
\[ \text{Total uncertainty} = \text{Uncertainty in } R_1 + \text{Uncertainty in } R_2 = 3 \, \Omega + 4 \, \Omega = 7 \, \Omega \]

### Step 5: Write the final result
Thus, the equivalent resistance with its uncertainty is:
\[ R_{eq} = 300 \, \Omega \pm 7 \, \Omega \]

### Final Answer:
The equivalent resistance of the series combination is \( 300 \pm 7 \, \Omega \).

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