Assertion : The dimensional formula for product of resistance and conductance is same as for dielectric constant.
Reason : both have dimensions of time constant.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true but reason is not the correct explanation of assertion
C. If assertion is true but reason is false
D. If both assertion and reason are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason given.

### Step 1: Understanding the Assertion
The assertion states that the dimensional formula for the product of resistance (R) and conductance (G) is the same as that for the dielectric constant (k).

- **Resistance (R)** has the dimensional formula:
\[ R = \frac{V}{I} = \frac{ML^2T^{-3}}{I^2} \]
where \( V \) is voltage, \( I \) is current, and the dimensions of voltage are \( ML^2T^{-3}I^{-1} \).

- **Conductance (G)** is the reciprocal of resistance:
\[ G = \frac{1}{R} \]
Thus, the dimensional formula for conductance is:
\[ G = \frac{I^2}{ML^2T^{-3}} \]

- The product of resistance and conductance is:
\[ R \cdot G = R \cdot \frac{1}{R} = 1 \]
Therefore, the dimensional formula for the product of resistance and conductance is:
\[ [R \cdot G] = [1] = M^0L^0T^0 \]
This means it is dimensionless.

### Step 2: Understanding the Dielectric Constant
The dielectric constant (k) is defined as the ratio of the capacitance of a capacitor with a dielectric medium to the capacitance of the same capacitor in a vacuum.

- The dielectric constant is also dimensionless:
\[ k = \frac{C_{medium}}{C_{vacuum}} \]
Since both capacitances have the same dimensions, the dielectric constant has no dimensions, hence:
\[ [k] = M^0L^0T^0 \]

### Step 3: Conclusion on the Assertion
Since both the product of resistance and conductance and the dielectric constant are dimensionless, the assertion is true.

### Step 4: Analyzing the Reason
The reason states that both have dimensions of the time constant.

- The time constant (τ) in an RC circuit is given by:
\[ τ = R \cdot C \]
where \( C \) is capacitance. The dimensions of time constant are:
\[ [τ] = [R][C] = [R][\frac{Q}{V}] = [R][\frac{I \cdot T}{V}] \]
This shows that the time constant has dimensions, while both the product of resistance and conductance and the dielectric constant do not.

### Final Conclusion
- The assertion is true: the dimensional formula for the product of resistance and conductance is the same as for the dielectric constant.
- The reason is false: they do not have dimensions of time constant.

### Answer:
- Assertion: True
- Reason: False

### Correct Option:
- The correct option is the third one.

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