Two resistors of 10K`Omega` and 20K`Omega` are conne cted in series. If tolerance of each resistor is 10% then tolerance of the combination will be

Options

A. 0.05
B. 0.1
C. 0.15
D. 0.2

Answer

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

### Step-by-Step Solution:

1. **Identify the Resistors and Their Values:**
- Let \( R_1 = 10 \, \text{k}\Omega \) (10,000 ohms)
- Let \( R_2 = 20 \, \text{k}\Omega \) (20,000 ohms)

2. **Determine the Tolerance of Each Resistor:**
- The tolerance for each resistor is given as 10%. This means:
- For \( R_1 \): \( \text{Tolerance} = 10\% \) of \( 10 \, \text{k}\Omega = 0.1 \times 10,000 = 1,000 \, \Omega \)
- For \( R_2 \): \( \text{Tolerance} = 10\% \) of \( 20 \, \text{k}\Omega = 0.1 \times 20,000 = 2,000 \, \Omega \)

3. **Calculate the Effective Resistance of the Series Combination:**
- The total resistance \( R_s \) in series is given by:
\[ R_s = R_1 + R_2 = 10 \, \text{k}\Omega + 20 \, \text{k}\Omega = 30 \, \text{k}\Omega \]

4. **Calculate the Total Tolerance for the Series Combination:**
- The tolerance for resistors in series adds up. Therefore, the total tolerance \( T \) is:
\[ T = \text{Tolerance of } R_1 + \text{Tolerance of } R_2 = 1,000 \, \Omega + 2,000 \, \Omega = 3,000 \, \Omega \]

5. **Calculate the Percentage Tolerance of the Total Resistance:**
- The percentage tolerance of the total resistance is calculated as:
\[ \text{Percentage Tolerance} = \left( \frac{T}{R_s} \right) \times 100 = \left( \frac{3,000 \, \Omega}{30,000 \, \Omega} \right) \times 100 = 10\% \]

6. **Final Result:**
- The tolerance of the combination of the two resistors in series is 10%.

### Summary:
The tolerance of the combination of the two resistors connected in series is 10%.