Two resistors of resistances `R_(1)=(300+-3) Omega` and `R_(2)=(500+-4) Omega ` are connected in series. The equivalent resistance of the series combination is

Options

A. `(800+-1)Omega`
B. `(800+-7)Omega`
C. `(200+-7)Omega`
D. `(200+-1)Omega`

Explanation

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

### Step-by-Step Solution:

1. **Identify the resistances and their uncertainties:**
- The first resistor \( R_1 = 300 \, \Omega \) with an uncertainty of \( \pm 3 \, \Omega \).
- The second resistor \( R_2 = 500 \, \Omega \) with an uncertainty of \( \pm 4 \, \Omega \).

2. **Calculate the equivalent resistance in series:**
- The formula for equivalent resistance \( R \) in series is:
\[ R = R_1 + R_2 \]
- Substituting the values:
\[ R = 300 \, \Omega + 500 \, \Omega = 800 \, \Omega \]

3. **Calculate the total uncertainty:**
- When resistors are added in series, the uncertainties also add up. Therefore, the total uncertainty \( \Delta R \) is given by:
\[ \Delta R = \Delta R_1 + \Delta R_2 \]
- Substituting the uncertainties:
\[ \Delta R = 3 \, \Omega + 4 \, \Omega = 7 \, \Omega \]

4. **Combine the results:**
- Thus, the equivalent resistance with its uncertainty is:
\[ R = 800 \, \Omega \pm 7 \, \Omega \]

5. **Final Answer:**
- The equivalent resistance of the series combination is:
\[ R = 800 \pm 7 \, \Omega \]