Manipal MET2014PhysicsUnits and Dimensions
- If L, C and R denote the inductance, capacitance and resistance respectively, the dimensional formula for C^2 L R is
Options
- A[ ML ⁻² ~T ⁻¹ I ^0 ]
- B[M^0 L^0 T^3 I^0 ]
- C[M⁻¹ L⁻² T^6 I^2 ]
- D[M^0 L^0 T^2 I^0 ]
Correct answer
B. [M^0 L^0 T^3 I^0 ]
Step-by-step solution
Given, [C^2 L R ]= [C^2 L^2 R L ]= [(L C)^2 ( R L ) ] and we know that frequency of L C circuits f= 1 2 1 L C . Here the dimension of L C is equal to [ T ^2 ] . [ L R ] gives the time constant of L-R circuit, so that the dimension of L R is equal to .T T ] . Hence the required dimensions [(L C)^2 ( R L ) ]= [T^2 ]^2 [T⁻¹ ]= [T^3 ] .