JEE MainPhysicsUnits and Dimensions
A physical quantity is measured in the compound SI unit Farad Volt ^2 Ampere ⁻¹ meter ⁻¹ . The dimensional formula of this quantity is
Options
- A[L⁻¹ T]
- B[M L T⁻² A⁻¹]
- C[M L^2 T⁻² A⁻¹]
- D[M L^3 T⁻² A]
Correct answer
B. [M L T⁻² A⁻¹]
Step-by-step solution
The given unit can be written as Farad Volt ^2 Ampere meter . The energy stored in a capacitor is given by U = 1 2 CV^2 . Therefore, the product of Farad (unit of capacitance) and Volt ^2 corresponds to the unit of energy (Joule). Dimensions of Energy = [M L^2 T⁻²] The denominator has the units Ampere meter , which has the dimensions [A L] . Substituting these into the given expression: Dimensional formula = [M L^2 T⁻²] [A L] = [M L T⁻² A⁻¹] Answer: [M L T⁻² A⁻¹]