Dielectric constant has the same dimensions as

Options

A. Stress
B. Strain
C. Electric capacity
D. Electric permittivity

Answer

To solve the question regarding the dielectric constant and its dimensions, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Dielectric Constant**: The dielectric constant (k) of a material is defined as the ratio of the capacitance of a capacitor filled with the dielectric material to the capacitance of the same capacitor when it is filled with air (or vacuum). Mathematically, it can be expressed as:
\[ k = \frac{C_{\text{dielectric}}}{C_{\text{air}}} \]

2. **Nature of Dielectric Constant**: Since the dielectric constant is a ratio of two capacitances, it is a dimensionless quantity. Capacitance itself has units (Farads), but when you take a ratio of two capacitances, the units cancel out, leaving a pure number without any dimensions.

3. **Identifying Dimensionless Quantities**: To find a quantity that has the same dimensions as the dielectric constant, we need to look for other dimensionless quantities.

4. **Example of Dimensionless Quantities**: One common example of a dimensionless quantity is strain. Strain is defined as the change in length divided by the original length:
\[ \text{Strain} = \frac{\Delta L}{L} \]
Here, both \(\Delta L\) (change in length) and \(L\) (original length) have the same dimensions (length), so when you take their ratio, the dimensions cancel out, making strain a dimensionless quantity.

5. **Conclusion**: Since the dielectric constant is dimensionless and strain is also dimensionless, we conclude that the dielectric constant has the same dimensions as strain.

### Final Answer:
The dielectric constant has the same dimensions as strain, which is a dimensionless quantity.

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