Question

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

Answer 1

In simple way, you can solve this by using formula,
$\bold{\nu=\frac{1}{2\pi\sqrt{LC}}}$
where , ν is the frequency ,
L is the inductance
C is the capacitance,

you know, SI unit of frequency , e.g., Hz or cycle /sec
so,$\bold{\nu=\frac{1}{2\pi\sqrt{LC}}}\\\\\nu^2=\frac{1}{4\pi^2LC}$
here π² and 4 are constant .
∴ SI unit of LC = SI unit of 1/ν² or Si unit of (1/ν)²
we know, SI unit of inverse of frequency is second .
Then, SI unit of LC = (sec²)

Or you can find by using SI unit of capacitance and inductance ,
SI unit of capacitance = Farad
SI unit of inductance = Henry
so, SI unit of LC = Farad.Henery


[ Actually, Farad = s⁴.A².m⁻².Kg⁻¹ and Henry = Kg.m².A⁻².s⁻² , then Farad.Henry = s² = (sec)² ]