When a lossy capacitor with a dielectric of permittivity

When a lossy capacitor with a dielectric of permittivity ε and conductivity σ operates at a frequency ω, the loss tangent for the capacitor is given by—

tan δ =	I_R	=	V
	I_c		RVωC

= 1/ωCR
C = A∈/d,
R = d/σA

∴ CR =	A_∈	d	=	∈
∴ CR =	d	σA	=	σ

∴ tan δ =	1	=	∈
	ω∈/σ		ω∈