A resistor of `6kOmega`with tolerance 10% and another resistance of `4kOmega` with tolerance `10%` are connected in series. The tolerance of the combination is about

Options

A. `10%`
B. `20%`
C. `30%`
D. `40%`

Answer

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

### Step 1: Identify the values of the resistors and their tolerances.
- Resistor \( R_1 = 6 \, k\Omega \) with a tolerance of \( 10\% \).
- Resistor \( R_2 = 4 \, k\Omega \) with a tolerance of \( 10\% \).

### Step 2: Calculate the absolute tolerances for each resistor.
The absolute tolerance (change in resistance) can be calculated using the formula:
\[ \Delta R = \left( \frac{\text{Tolerance \%}}{100} \right) \times R \]

For \( R_1 \):
\[ \Delta R_1 = \left( \frac{10}{100} \right) \times 6 \, k\Omega = 0.6 \, k\Omega \]

For \( R_2 \):
\[ \Delta R_2 = \left( \frac{10}{100} \right) \times 4 \, k\Omega = 0.4 \, k\Omega \]

### Step 3: Calculate the total resistance in series.
When resistors are connected in series, the total resistance \( R \) is the sum of the individual resistances:
\[ R = R_1 + R_2 = 6 \, k\Omega + 4 \, k\Omega = 10 \, k\Omega \]

### Step 4: Calculate the total tolerance for the combination.
The total tolerance for resistors in series is the sum of their absolute tolerances:
\[ \Delta R_{\text{total}} = \Delta R_1 + \Delta R_2 = 0.6 \, k\Omega + 0.4 \, k\Omega = 1 \, k\Omega \]

### Step 5: Calculate the percentage tolerance of the combined resistance.
The percentage tolerance for the total resistance can be calculated using the formula:
\[ \text{Tolerance \%} = \left( \frac{\Delta R_{\text{total}}}{R} \right) \times 100 \]
Substituting the values:
\[ \text{Tolerance \%} = \left( \frac{1 \, k\Omega}{10 \, k\Omega} \right) \times 100 = 10\% \]

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

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