Dimensional formula of R2C/L

Resistance (R), capacitance (C), and inductance (L) are all physical quantities with their own units and dimensions. The dimensional formula of R2C/L can be derived by analyzing the units and dimensions of each of these quantities.

Unit and Dimension of Resistance (R)

The unit of resistance is ohm (Ω) and its dimension is [M*L2*T-3*A-2], where M represents mass, L represents length, T represents time, and A represents electric current.

Unit and Dimension of Capacitance (C)

The unit of capacitance is farad (F) and its dimension is [M^-1*L^-2*T^4*A^2], where M represents mass, L represents length, T represents time, and A represents electric current.

Unit and Dimension of Inductance (L)

The unit of inductance is henry (H) and its dimension is [M*L^2*T^-2*A^-2], where M represents mass, L represents length, T represents time, and A represents electric current.

Deriving the Dimensional Formula of R2C/L

To find the dimensional formula of R2C/L, we first need to square the resistance (R2) and divide it by the product of capacitance (C) and inductance (L).

Therefore,

R2C/L = [(Ω)2 * F-1 * H-1]

= Ω2 * F-1 * H-1

= [M*L2*T-3*A-2]2 * [M^-1*L^-2*T^4*A^2]^-1 * [M*L^2*T^-2*A^-2]^-1

= [M2*L4*T^-6*A^-4] * [M*L^2*T^-2*A^-2] * [M^-1*L^2*T^-4*A^-2]

= [M2*L^4*T^-6*A^-4] * [M^-1*L^2*T^-2*A^-2] * [M^-1*L^2*T^-4*A^-2]

= [M0*L^4*T^-6*A^-4]

Conclusion

The dimensional formula of R2C/L is [M0*L^4*T^-6*A^-4]. This means that R2C/L has no dimension of mass, a dimension of length raised to the power of 4, a dimension of time raised to the power of negative 6, and a dimension of electric current raised to the power of negative 4.