99 Percentile Qs Bank for JEE MainPhysicsUnits and Dimensions
If C, R, L and I denote capacity, resistance, inductance and electric current respectively, the quantities having the same dimensions of time are : (1) C R (2) L R (3) L C (4) L I^2
Options
- A(1) and (2) only
- B(1) and (3) only
- C(1) and (4) only
- D(1), (2) and (3) only
Correct answer
D. (1), (2) and (3) only
Step-by-step solution
[C]= [ M ⁻¹ ~L ⁻² ~T ^4 ~A ^2 ],[R]= [ M L ^2 ~T ⁻³ ~A ⁻² ][L]= [ ML ^2 ~T ⁻² ~A ⁻² ] and [I]= [ M ^0 ~L ^0 ~T ^0 ~A ] (1) [C R]= [ M ⁻¹ ~L ⁻² ~T ^4 ~A ^2 ] [ ML ^2 ~T ⁻³ ~A ⁻² ]= [ M ^0 ~L ^0 TA ^0 ] (2) [ L R ]= [ ML ^2 ~T ⁻² ~A ⁻² ] [ ML ^2 ~T ⁻³ ~A ⁻² ] = [ M ^0 ~L ^0 TA ^0 ] (3) [ L C ]= ( [ ML ^2 ~T ⁻² ~A ⁻² ] [ M ⁻¹ ~L ⁻² ~T ^4 ~A ^2 ] )^ 1 / 2 = [ M ^0 ~L ^0 TA ^0 ] (4) [L I^2 ]= [ ML ^2 ~T ⁻² ~A ⁻² ] [ M ^0 ~L ^0 ~T ^0 ~A ^0 ]^2= [ ML ^2 ~T ⁻² ~A ^0 ] Hence, option (d) is correct.