COMEDK2023Morning ShiftPhysicsCapacitanceActual
If C be the capacitance and V be the electric potential, then the dimensional formula of CV ^2 is
Options
- A[ ML ^2 ~T ⁻² ~A ^0 ]
- B[ M ^0 LT ⁻² ~A ^0 ]
- C[ ML ⁻³ TA ]
- D[ MLT ⁻² ~A ⁻¹ ]
Correct answer
A. [ ML ^2 ~T ⁻² ~A ^0 ]
Step-by-step solution
The energy U stored in a capacitor is given by the formula U = 1 2 CV^2 . Since U represents energy, its dimensional formula is the same as that of work or energy, which is [ML^2T⁻²] . The factor 1 2 is a dimensionless constant and does not affect the dimensions. Therefore, the dimensional formula of CV^2 is the same as the dimensional formula of energy, which is [ML^2T⁻²A^0] . Answer: [ ML ^2 ~T ⁻² ~A ^0 ]