A parallel plate condenser has a capacitance `50 muF` in air and `110 muF` when immersed in an oil. The dielectric constant `k` of the oil is

Options

A. 0.45
B. 0.55
C. `1.10`
D. `2.20`

Answer

To find the dielectric constant \( k \) of the oil used in the parallel plate capacitor, we can use the relationship between capacitance in air and capacitance in a dielectric medium.

### Step-by-Step Solution:

1. **Understand the Capacitance Formula**:
The capacitance \( C \) of a parallel plate capacitor is given by the formula:
\[ C = k \cdot C_0 \]
where \( C_0 \) is the capacitance in air (or vacuum) and \( k \) is the dielectric constant of the medium.

2. **Identify Given Values**:
From the problem, we have:
- Capacitance in air, \( C_0 = 50 \, \mu F \)
- Capacitance in oil, \( C = 110 \, \mu F \)

3. **Set Up the Equation**:
Using the relationship between the capacitance in air and the capacitance in oil, we can write:
\[ C = k \cdot C_0 \]
Substituting the known values:
\[ 110 \, \mu F = k \cdot 50 \, \mu F \]

4. **Solve for \( k \)**:
To find \( k \), rearrange the equation:
\[ k = \frac{C}{C_0} = \frac{110 \, \mu F}{50 \, \mu F} \]
Now perform the division:
\[ k = \frac{110}{50} = 2.2 \]

5. **Conclusion**:
The dielectric constant \( k \) of the oil is:
\[ k = 2.2 \]

### Final Answer:
The dielectric constant \( k \) of the oil is \( 2.2 \).

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