The resistors of resistances `R_(1)=100pm3" ohm and R"_(2)=200pm 4ohm` are connected in series. The equivalent resistance of the series combination is

Options

A. `300 pm 5Ohm`
B. `300 pm 7Ohm`
C. `300pm 9 Ohm`
D. `300 pm 3Ohm`

Explanation

To find the equivalent resistance of two resistors connected in series, we can use the formula for equivalent resistance and also account for the uncertainties in the measurements.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Resistance \( R_1 = 100 \pm 0.3 \, \text{ohm} \)
- Resistance \( R_2 = 200 \pm 4 \, \text{ohm} \)

2. **Calculate the Equivalent Resistance:**
- For resistors in series, the equivalent resistance \( R_{\text{eq}} \) is given by:
\[ R_{\text{eq}} = R_1 + R_2 \]
- Substitute the values:
\[ R_{\text{eq}} = 100 + 200 = 300 \, \text{ohm} \]

3. **Calculate the Total Uncertainty:**
- The total uncertainty in the equivalent resistance when adding two resistances is the sum of their individual uncertainties:
\[ \Delta R_{\text{eq}} = \Delta R_1 + \Delta R_2 \]
- Substitute the uncertainties:
\[ \Delta R_{\text{eq}} = 0.3 + 4 = 4.3 \, \text{ohm} \]

4. **Combine the Results:**
- The equivalent resistance with its uncertainty is:
\[ R_{\text{eq}} = 300 \pm 4.3 \, \text{ohm} \]

### Final Answer:
The equivalent resistance of the series combination is:
\[ R_{\text{eq}} = 300 \pm 4.3 \, \text{ohm} \]