Question

What is the SI unit of LC? (L=Inductance and C=Capacitance)

Answer 1

We know that resonant frequency for a LC circuit is f= 1/2pi root (LC). And pi doesnt have units. So basically the unit of LC from this is derived as (seconds)^2.
or
In the simplest way possible:

L is in henries (H) - Ω⋅sΩ⋅sΩ⋅s.

C is in farads (F) - sΩsΩ

Answer 2

The SI unit of LC is s^2

• Inductance: Inductance is the tendency of an electric conductor to oppose the change in the electric current flowing through it.
• The formula for inductance is given as

                      L = V/(di/dt)

                      L = inductance

                      V = voltage

                      di/dt = change in current

• If V is measured in volts, i is measured in amperes(coulomb/s), t is measured in seconds then

         units of L = volt/(A/s) = Henry(H) = V/(Coulomb/s)/s = Vs^2/Coulomb

• Capacitance: Capacitance is the property of a system that enables it to store charge.
• The formula of capacitance is given by

                      C = q/V

                      C = capacitance

                      q = charge

                      V = voltage

• If q is measured in coulombs and voltage in volts then

        units of C = Coulombs/Volts = Farads

• Therefore, SI unit of LC = (Vs^2/Coulomb)x(Coulomb/V)

                                                = s^2