Here is an extensive table of impedance, admittance, magnitude, and phase angle equations (formulas) for fundamental
series and parallel combinations of resistors, inductors, and capacitors. All schematics and equations assume
ideal components, where resistors exhibit only resistance, capacitors exhibit only capacitance, and inductors
exhibit only inductance.
For those unfamiliar with complex numbers,
the "±j" operator signifies a phase of ±90°. Voltage across a capacitor lags the current through it by 90°, so
j is used along with its capacitive reactance (j/ωC). Voltage across
an inductor leads the current through it by 90°, so +j is used along with
inductive reactance (jωL).
"M" is the mutual inductance between inductors.
"ω" is frequency in radians/second, and is equal to 2π
times frequency in cycles/second.
This is probably one of the most comprehensive collections you will find on the Internet.
Z = R + jX
Z = (R^{2} + X^{2})^{½}
ϕ = tan^{1}(X/R)
Y = 1/Z

R 
R 
0 
1/R 

jωL 
ωL 
+π/2 
j/ωL 

j/ωC 
1/ωC 
π/2 
jωC 

jω(L_{1}+L_{2}±2M) 
ω(L_{1}+L_{2}±2M) 
+π/2 
j/[ω(L_{1}+L_{2}±2M)] 

(j/ω)(1/C_{1}+1/C_{2}) 
(1/ω)(1/C_{1}+1/C_{2}) 
π/2 
jωC_{1}C_{2}/(C_{1}+C_{2}) 

R+jωL 
(R^{2}+ω^{2}L^{2})^{½} 
tan^{1}(ωL/R) 
(RjωL)/(R^{2}+ω^{2}L^{2}) 

Rj/ωC 
(1/ωC)(1+ω^{2}C^{2}R^{2})^{½} 
tan^{1}(1/ωCR) 
(R+j/ωC)/(R^{2}+1/ω^{2}C^{2}) 

j(ωL1/ωC) 
(ωL1/ωC) 
±π/2 
jωC/(1ω^{2}LC) 

R+j(ωL1/ωC) 
[R^{2}+(ωL1/ωC)^{2}]^{½} 
tan^{1}[(ωL1/ωC)/R] 


R_{1}R_{2}/(R_{1}+R_{2}) 
R_{1}R_{2}/(R_{1}+R_{2}) 
0 
1/R_{1}+1/R_{2} 



+π/2 


j/ω(C_{1}+C_{2}) 
1/ω(C_{1}+C_{2}) 
π/2 
jω(C_{1}+C_{2}) 


ωLR/(R^{2}+ω^{2}L^{2})^{½} 
tan^{1}(R/ωL) 
1/Rj/ωL 

R(1jωCR)/(1+ω^{2}C^{2}R^{2}) 
R/(1+ω^{2}C^{2}R^{2})^{½} 
tan^{1}(ωCR) 
1/R+jωC 

jωL/(1ω^{2}LC) 
ωL/(1ω^{2}LC) 
±π/2 
j(ωC1/ωL) 


[(1/R)^{2}+(ωC1/ωL)^{2}]^{½} 
tan^{1}[R(1/ωLωC)] 
1/R+j(ωC1/ωL) 

Impedance Z 

Magnitude Z 

Phase Angle ϕ 

Admittance 


Impedance Z 

Magnitude Z 

Phase Angle ϕ 

Admittance 


Impedance Z 

Magnitude Z 

Phase Angle ϕ 

Admittance 


Impedance Z 

Magnitude Z 

Phase Angle ϕ 

Admittance 


Impedance Z 

Magnitude Z 

Phase Angle ϕ 
tan^{1}(X_{1}/R_{1})+tan^{1}(X_{2}/R_{2})tan^{1}[(X_{1}+X_{2})/(R_{1}+R_{2})] 
Admittance 
1/(R_{1}+jX_{1})+1/(R_{2}+jX_{2}) 
Note: Corrections made to RLC Magnitude and Admittance formulas, and to RLR Admittance formula on 7/3/2014.
Thanks to Bob N. for catching the errors.
(source: Reference Data for Engineers, 1993)
