The dimensional formula for capacitance is ________.

• (A). M¹L^-2T^-2Q^-2
• (B). M¹L²T^-2Q^-2
• (C). M¹L^-2T²Q²
• (D). M^-1L^-2T²Q²

The dimensional formula for capacitance is an important concept in physics, particularly in the study of electrical circuits. To determine the correct dimensional formula, we first need to understand what capacitance is and how it relates to other physical quantities.

Understanding Capacitance

Capacitance is defined as the ability of a system to store electric charge per unit voltage. Mathematically, it is expressed as:

C = Q/V

Where:

• C is the capacitance measured in farads (F).
• Q is the electric charge measured in coulombs (C).
• V is the voltage measured in volts (V).

Breaking Down Voltage

Voltage (V) can be further broken down into its fundamental dimensions. Voltage is defined as energy per unit charge:

V = W/Q

Where:

• W is energy, which has the dimensional formula of M L² T^-2.

Thus, we can express voltage in terms of its dimensions:

V = (M L² T^-2)/Q

Finding the Dimensional Formula for Capacitance

Now, substituting the expression for voltage back into the formula for capacitance:

C = Q/(M L² T^-2/Q)

This simplifies to:

C = Q²/(M L² T^-2)

Rearranging gives us:

C = M^-1 L^-2 T² Q²

Final Answer

From the options provided, the correct dimensional formula for capacitance is:

(D) M^-1 L^-2 T² Q²

Summary

In summary, capacitance is fundamentally linked to charge and voltage, and through dimensional analysis, we find that its dimensional formula is M^-1 L^-2 T² Q². This understanding is crucial for further studies in electromagnetism and circuit theory.