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`

Explanation

To find the dielectric constant \( k \) of the oil used in the parallel plate capacitor, we can follow these steps:

### Step 1: Understand the relationship between capacitance and dielectric constant
The capacitance \( C \) of a parallel plate capacitor in air is given as \( C_0 \). When a dielectric material is introduced, the capacitance becomes \( C = k \cdot C_0 \), where \( k \) is the dielectric constant of the material.

### Step 2: Identify given values
From the problem, we have:
- Capacitance in air, \( C_0 = 50 \, \mu F \)
- Capacitance in oil, \( C = 110 \, \mu F \)

### Step 3: Write the equation for the dielectric constant
Using the relationship from Step 1, we can express the dielectric constant \( k \) as:
\[ k = \frac{C}{C_0} \]

### Step 4: Substitute the known values into the equation
Now, substituting the values we have:
\[ k = \frac{110 \, \mu F}{50 \, \mu F} \]

### Step 5: Simplify the equation
Calculating the right-hand side:
\[ k = \frac{110}{50} = 2.2 \]

### Step 6: State the final answer
Thus, the dielectric constant \( k \) of the oil is:
\[ k = 2.2 \]

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