Useful Formulae

Electrical symbols and units

Quantity Symbol Unit Abbreviated units

Angle  radian or degree Rad or 
Capacitance C Farad F
Charge Q Coulomb C
Conductance G Siemen S
Current I Ampere A
Energy J Joule J
Flux  Weber Wb
Flux density B Tesla T
Frequency f Hertz Hz
Impedance Z Ohm Ω
Inductance L Henry H
Power P Watt W
Reactance X Ohm Ω
Resistance R Ohm Ω
Time t second s
Voltage V Volt V

Charge, current and voltage

Q=It

Ohm’s Law

V=IR and I=V/R and R=V/I

Similarly if resistance is replaced by reactance or
impedance:

V=IX and I=V/X and X=V/I

V=IZ and I=V/Z and Z=V/I

Power and energy

P=IV and P = V2 / R and P = I2 R

J = P  t and since P=IV so J=IVt

1
Resistors in series

RT = R 1 + R2 + R3

Resistors in parallel

1 1 1 1 R1  R2
   but where there are only two resistors RT 
RT R1 R2 R3 R1  R2

Capacitance

A
C where  is the permittivity of the dielectric and  = 0 r
d
Capacitance, charge and voltage

Q=CV

Inductance

A
L  n2 where µ is the permeability of the magnetic medium and µ = µ0 µr
l
Energy stored in a capacitor

J = ½ C V2

Energy stored in an inductor

J = ½ L I2

Inductors in series

LT = L1 + L2 + L3

Inductors in parallel

1 1 1 1 L1  L2
   but where there are only two inductors LT 
LT L1 L2 L3 L1  L2

Capacitors in series

1 1 1 1 C1  C2
   but where there are only two capacitors CT 
CT C1 C2 C3 C1  C2

Capacitors in parallel

CT = C1 + C2 + C3

2
Induced e.m.f. in an inductor

di di
e  L where is the rate of change of current with time
dt dt
Current in a capacitor

dv dv
iC where is the rate of change of voltage with time
dt dt

Sine wave voltage

v = Vmax sin( t) or v = Vmax sin(2  f t) because =2f

f=1/T where T is the periodic time

For a sine wave, to convert:

RMS to peak multiply by 1.414
Peak to RMS multiply by 0.707
Peak to average multiply by 0.636
Peak to peak-peak multiply by 2

Capacitive reactance Inductive reactance

VC 1 VL
XC = = XL = = 2fL
IC 2fC IL

Resistance and reactance in series

 X
Z= R2  X 2  and  = arctan  
 R

Resonance
1 1
XL = X C thus L = or 2 fo L =
C 2foC
1
fo =
2 LC
L fo
Q= Bandwidth =
R Q

Power factor
Power factor = True power/Apparent power = Watts / Volt-amperes = W / VA

True power = V  (I  cos ) = V I cos  Power factor = cos  = R / Z

Reactive power = V  (I  sin ) = V I sin 

3
Bipolar junction transistors (BJT)

Transistor junction current equation IE = IB + IC

IC
Large signal (or d.c.) common emitter current gain hFE 
IB

I C
Small signal (or a.c.) common emitter current gain h fe  (Δ is a small change)
I B

Collector power dissipation PC = IC × VCE

Total power dissipation PT = PC + PB = (IC × VCE) + (IB × VBE)

PT ≈ IC × VCE when hFE is large

Junction gate field effect transistors (JFET)

ID
Large signal (or d.c.) common source forward transfer conductance g FS 
VGS
I D
Small signal (or a.c.) common source forward transfer conductance gfs 
VGS
Total power dissipation PT = ID × VDS

Power supplies

Vout
Output resistance Rout 
I out

 V 
Regulation =  out  100%
 Vin 

Amplifiers

Vout I out Pout

Voltage gain Av  Current gain Ai  Power gain Ap   Ai  Av
Vin I in Pin

Av 1
Gain with negative feedback G  (when β is large, G  )
1   Av 

4
Generalised small signal hybrid (h-) parameters

Vin Vin
Input resistance hi  Reverse transfer voltage ratio hr 
I in Vout

I out I out
Forward current transfer ratio hf  Output conductance ho 
I in Vout

Common emitter small signal h-parameters

Vbe Vbe
Input resistance hie  Reverse transfer voltage ratio hre 
I b Vce

I c I c
Forward current transfer ratio hfe  Output conductance hoe 
I b Vce

hfe RL
Common emitter amplifier voltage gain Av 
hie

Operational amplifiers

Vout V 
Voltage gain Av  or Av  20log10  out  dB
Vin  Vin 

Vbe Vout RF
Slew rate  Inverting amplifier voltage gain Av  
t Vin RIN

1 0.159
Lower cut-off frequency of an inverting amplifier f1  
2 CIN RIN CIN RIN

1 0.159
Upper cut-off frequency of an inverting amplifier f 2  
2 CF RF CF RF

 1   1   1 1 
Bandwidth f 2  f1      0.159   
 2 CF RF   2 CIN RIN   CF RF CIN RIN 

5
Oscillators

Av
Gain with positive feedback G  (when βAV →1, G →∞)
1   Av

1
Ladder network oscillator (with three CR sections) f 
2 6CR

1
Wien bridge oscillator (with C=C1=C2= and R=R1=R2) f 
2 CR

Av 1
Gain with negative feedback G  (when β is large, G  )
1   Av 

Astable multivibrator (with C=C1=C2= and R=R1=R2) T = 1.4 CR

Timers

Monostable mode T = 1.1 CR

Astable mode ton = 0.693C(R1+R2) toff = 0.693CR2 T = ton+toff = 0.693C(R1+2R2)

1.44
Pulse repetition frequency p.r. f . 
C ( R1  2 R2 )

ton R1  R2
Mark to space ratio  
toff R2

ton R  R2
Duty cycle =  1 100%
ton  toff R1  2 R2

Transformers

Flux equation   max sin(2 ft )

Primary voltage Vp  4.44 fNpmax Secondary voltage Vs  4.44 fNsmax

Vp Np Np Ns
Voltage and turns ratio  Turns per volt  
Vs Ns Vp Vs

For more information and other resources please go to: http://www.key2electronics.com