Formulas for Tesla coils

On this page are listed Tesla coil formulas for a reference to those who prefer to make calculations on paper. Below is a table of formulas on this page.

 Ohm's Law Transformer Input and Output Capacitive Reactance Inductive Reactance Resonant Circuit Formula Spiral Coil Helical Coil Inverse Conical Coil Secondary Coil Dimensions Medhurst Toroid Capacitance Sphere Capacitance Plate Capacitors Leyden Jar Capacitors AC RMS/Peak Voltage Rotary Gap Firing Rotary Gap Electrode Speed Energy for L and C

Ohm's Law

E = IZ                 P = IE

E = volts

I = current in amps

Z = impedance or resistance in ohms

P = power in watts

Transformer Input and Output

EpIp = EsIs

EP = primary voltage

IP = primary current in amps

ES = secondary voltage

IS = secondary current in amps

Capacitive Reactance

XC = capacitive reactance in ohms

F = frequency in hertz

C = capacitance in farads

Inductive Reactance

XL = inductive reactance in ohms

F = frequency in hertz

L = inductance in henrys

Resonant Circuit Formula

F = frequency in hertz

L = inductance in henrys

C = capacitance in farads

Spiral Coil Inductance

L = inductance of coil in microhenrys (µH)

R = average radius of the coil in inches

N = number of turns

W = width of the coil in inches

Helical Coil Inductance

L = inductance of coil in microhenrys (µH)

N = number of turns

R = radius of coil in inches (Measure from the center of the coil to the middle of the wire.)

H = height of coil in inches

Inverse Conical Coil Inductance

L = inductance of coil in microhenrys (µH)

L1 = helix factor

L2 = spiral factor

N = number of turns

R = average radius of coil in inches

H = effective height of the coil in inches

W = effective width of the coil in inches

X = rise angle of the coil in degrees

Secondary Coil Dimensions

T = AH

L = length of wire in feet

D = outer diameter of coil form in inches

H = height of windings in inches

A = number of turns per inch

T = total number of turns

B = thickness of wire in inches

Medhurst

C = self capacitance in picofarads

R = radius of secondary coil in inches

L = length of secondary coil in inches

Toroid Capacitance

C = capacitance in picofarads

D1 = outside diameter of toroid in inches

D2 = diameter of cross section of toroid in inches

This equation courtesy Bert Pool.

Sphere Capacitance

C = capacitance in picofarads

R = radius in inches

Plate Capacitors

C = capacitance in microfarads

K = dielectric constant

A = area of each plate in square inches

N = number of plates

D = distance between plates in inches (thickness of dielectric)

Leyden Jar Capacitors

C = capacitance in microfarads

K = dielectric constant

D = diameter of jar in inches

H = height of jar in inches

T = thickness of jar in inches

AC RMS and Peak Voltage

ERMS = 0.7071·E P

ERMS = RMS voltage

EP = peak voltage

Rotary Spark Gap Firings per Second

F = firings per second (hertz)

R = motor RPM rating

E = number of rotary electrodes

Rotary Spark Gap Electrode Speed

S = electrode speed (MPH)

R = motor RPM rating

D = diameter of electrode placement circle (inches)

Energy for L and C

Capacitance           Inductance

J = 0.5 V2 C           J = 0.5 I2 L

J = joules of energy stored

V = peak charge voltage

I = peak current

C = capacitance in farads

L = inductance in henries

Peak values of V and I are stated in order to emphasize not to use RMS values. The energy stored at any given time is of course:

J(t) = 0.5 [V(t)]2 C and J(t) = 0.5 [I(t)]2 L.

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