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
Circuit Configuration 
Impedance Z = R + jX 
Magnitude {Z} = (R^{2} + X^{2})^{½} 
Phase Angle
ϕ = tan^{1}(X/R) 
Admittance 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)
