Assertion: The dimensional formula for the product of resistance and conductance is the dielectric constant.

Reason: Both resistance and conductance have dimensions of time constant.

Analysis:

To understand the assertion and reason in detail, let's analyze the dimensional formulas for resistance, conductance, and dielectric constant.

Dimensional formula for resistance (R):
Resistance is defined as the ratio of voltage (V) to current (I). The dimensional formula for voltage is [M^1 L^2 T^-3 I^-1] and for current is [I^1]. Therefore, the dimensional formula for resistance (R) can be calculated as:

R = V/I = [M^1 L^2 T^-3 I^-1] / [I^1] = [M^1 L^2 T^-3 I^-2]

Dimensional formula for conductance (G):
Conductance is the reciprocal of resistance. Therefore, the dimensional formula for conductance (G) will be the inverse of the dimensional formula for resistance (R). Hence,

G = 1/R = 1/([M^1 L^2 T^-3 I^-2]) = [M^-1 L^-2 T^3 I^2]

Dimensional formula for dielectric constant (ε):
The dielectric constant is a dimensionless quantity that represents the ratio of the capacitance of a capacitor with a dielectric material to the capacitance of the same capacitor with a vacuum as the dielectric. It does not have any dimensions.

Comparison:

Dimensional formula for product of resistance and conductance (RG):
To find the dimensional formula for the product of resistance and conductance, we multiply their respective dimensional formulas:

RG = R * G = ([M^1 L^2 T^-3 I^-2]) * ([M^-1 L^-2 T^3 I^2]) = [M^1 L^2 T^-3 I^-2] * [M^-1 L^-2 T^3 I^2] = [M^0 L^0 T^0 I^0]

Conclusion:

The dimensional formula for the product of resistance and conductance (RG) is dimensionless, which is the same as the dimensional formula for the dielectric constant (ε). Therefore, the assertion is correct.

Note:
The reason given, stating that both resistance and conductance have dimensions of time constant, is incorrect. Resistance and conductance have different dimensions, as shown in the analysis above.

Resistance x conductance = R x 1/R = (M0L0T0) = 1 and dielectric constant K is dimensionless. but of them do not have dimensions of time constant .
therefore asseration is correct but reason is incorrect.