COMEDK2019PhysicsUnits and Dimensions
The dimensional formula for inductance is
Options
- A[ ML ² ~T ⁻¹ ~A ⁻² ]
- B[ ML ² ~T ⁻² ~A ⁻¹ ]
- C[ ML ² ~T ⁻² ~A ⁻² ]
- D[ ML ² TA ⁻² ]
Correct answer
C. [ ML ² ~T ⁻² ~A ⁻² ]
Step-by-step solution
EMF induced in circular coil of self-inductance L is given by =-L d I d t EMF is equal to the potential difference dimensionally. Hence, =V We know, V= W q Thus, dimensional formula of potential difference is given as aligned V &= [M¹ L² T⁻² ] [A T] &= [M¹ L² T⁻³ A⁻¹ ] aligned The self-inductance is given by, L=V d t d I Dimensional formula of self-inductance is given by, L= [ M ¹ ~L ⁻² ~T ⁻³ ~A ⁻¹ ] [ T ] [ A ] Dimensional formula of self-inductance, L= [ M ¹ ~L ² ~T ⁻² ~A ⁻² ]