Below is a reference chart giving all the equations deriving from Ohm's Law. The parameters E, I, R and P are shown in the central area, each occupying one of the four quadrants of the pie. To solve for a given parameter, find that parameter at the center of the chart and choose the equation in its quadrant that defines the quantity in terms that you have measured or know.
- I = Electrical current in amperes
- E = Electrical potential in volts
- R = Resistance in ohms (Also sometimes "Z" or Impedance in ohms)
- P = Power in watts (Also sometimes "W")
Ohms Law (DC Current):
Current in amps = Voltage in volts / Resistance in ohms = Power in watts / Voltage in volts
Current in amps =
(Power in watts / Resistance in ohms)Voltage in volts = Current in amps × Resistance in ohms
Voltage in volts = Power in watts / Current in amps
Voltage in volts =
(Power in watts × Resistance in ohms)
Power in watts = (Current in amps)2 × Resistance in ohmsPower in watts = Voltage in volts × Current in amps
Power in watts = (Voltage in volts)2 / Resistance in Ohms
Resistance in ohms = Voltage in volts / Current in amps
Resistance in ohms = Power in watts / (Current in amps)2
Ohms Law (AC Current):
In the following AC Ohms Law formulas, q is the phase angle in degrees by which current lags voltage (in an inductive circuit) or by which current leads voltage (in a capacitive circuit). In a resonant circuit (such as normal household 120VAC) the phase angle is 0º and Impedance = Resistance.
Current in amps = Voltage in volts / impedance in ohms
Current in amps =
(Power in Watts / Impedance in ohms × cosq)Current in amps = Power in Watts / (Voltage in volts × cos q)
Voltage in volts = Current in amps × Impedance in ohms
Voltage in volts = Power in Watts / (current in amps × cos q)
Voltage in volts =
([Power in watts × Impedance in ohms] / cos q)Impedance in ohms = Voltage in volts / Current in amps
Impedance in ohms = Power in watts / (Current amps2 × cos q)
Impedance in ohms =(Voltage in volts2 × cos q) / Power in watts
Power in watts = Current in amps2 × Impedance in ohms × cos q
Power in watts = Current in amps × Voltage in volts × cos q
Power in watts = ([Voltage in volts]2 × cos q) / Impedance in ohms
ELECTRONIC CIRCUIT EQUATIONS:
Resonant frequency in hertz (where XL= XC) = 1 / (2p ×
[Inductance in henrys × Capacitance in farads])Reactance in ohms of an inductance is XL
XL = 2p(frequency in hertz × Inductance in henrys)
Reactance in ohms of a capacitance is XC
XC = 1 / (2p[frequency in hertz × Capacitance in farads] )
Impedance in ohms (series) =
(Resistance in ohms2 + (XL-XC)2) Impedance in ohms (parallel) = (Resistance in ohms × Reactance) / (Resistance in ohms2 + Reactance2
Resistors in Series (values in Ohms):
Total Resistance = Resistance1 + Resistance2 + ... Resistancen
Two Resistors in Parallel (values in Ohms):
Total Resistance = Resistance1 × Resistance2 / Resistance1 + Resistance2
Multiple Resistors in Parallel (values in Ohms):
Total Resistance = 1 / (1 / Resistance1] + 1 / Resistance2 + ... 1 / Resistancen])
Capacitors in Parallel (values in microfarads):
Total Capacitance in Parallel (values in any farad) = Capacitance1 + Capacitance2 + .... Capacitancen
Capacitors in Series (values in microfarads):
Total Capacitance in Series (values in any farad) = Capacitance1 × Capacitance2 / Capacitance1 + Capacitance2
Multiple Capacitors in Series (values in farads) = 1 / ([1 / Capacitance1] + [1 / Capacitance2] + ...... [1 / Capacitancen])
LCR Series Time Circuits:
Time in seconds = Inductance in henrys / Resistance in ohms
Time in seconds = Capacitance in farads × Resistance in ohms
Sine Wave Voltage and Current:
Effective (RMS) value = 0.707 × Peak value
Effective (RMS) value = 1.11 × Average value
Average value = 0.637 × Peak value
Average value = 0.9 × Effective (RMS) value
Peak Value = 1.414 × Effective (RMS) value
Peak Value = 1.57 × Average value
Decibels:
db = 10 Log10 (Power in Watts #1 / Power in Watts #2)
db = 10 Log10 (Power Ratio)
db = 20 Log10 (Volts or Amps #1 / Volts or Amps #2)
db = 20 Log10 (Voltage or Current Ratio)
Power Ratio = 10(db/10)
Voltage or Current Ratio = 10(db/20)
If impedances are not equal: db = 20 Log10 [(Volt1
[Z2]) / (Volt2 [Z1])] Frequency and Wavelength
Frequency in kilohertz = (300,000) /wavelength in meters
Frequency in megahertz = (300) / wavelength in meters
Frequency in megahertz = (964) / wavelength in feet
Wavelength in meters = (300,000) / frequency in kilohertz
Wavelength in meters = (300) / frequency in megahertz
Wavelength in feet = (964) / frequency in megahertz
Wavelength = speed of sound (ft/sec or m/sec) / frequency Speed of sound = 1130 ft/sec
Antenna Length:
Quarter-wave antenna: (ordinary wire, velocity factor = 0.95)
Length in feet = 234 / frequency in megahertz
Half-wave antenna: (ordinary wire, velocity factor = 0.95)
Length in feet = 466 / frequency in megahertz
70 Volt Loudspeaker Matching Transformer Primary Impedance = (Amplifier output volts)2 / Speaker Power
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