What is the dimensional formula of farad?

• A) [ M⁻¹L⁻²TQ ]
• B) [ M⁻¹L⁻²T²Q² ]
• C) [ M⁻¹L⁻²TQ² ]
• D) [ M⁻¹L⁻²T²Q ]

The dimensional formula of a farad, which is the unit of capacitance, can be derived from its definition. Capacitance is the ability of a system to store electric charge per unit voltage. The formula for capacitance (C) is given by:

C = Q/V

Where:

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

Breaking Down Voltage

Voltage (V) can be expressed in terms of energy (E) and charge (Q):

V = E/Q

Energy has the dimensional formula of [M L² T⁻²]. Thus, substituting this into the voltage formula gives:

Substituting for Voltage

Now, we can rewrite capacitance as:

C = Q / (E/Q) = Q² / E

Substituting the dimensional formula for energy:

Final Calculation

Thus, we have:

C = Q² / [M L² T⁻²]

Rearranging this leads to:

[M⁻¹ L⁻² T² Q²]

Therefore, the correct answer is:

B) [ M⁻¹L⁻²T²Q² ]