Formulas

Ohm's Law

:
E = I × R
I = E ÷ R
R = E ÷ I
Remember:
E = voltage, in Volts
I = current, in Amperes
R = resistance, in Ohms


Ohms Law for Series Circuits:

Resistance in Series:

Rt = R1 + R2 + R3 + .....

where:
      Rt = total resistance in series
      R1, R2 .... are individual resistors


Voltage in a Series Circuit:

Et = E1 + E2 + E3 ....

where:
      Et = total voltage applied to the circuit
      E1, E2, .... = the voltage drops across the individual resistors

Rule: In a series circuit the total voltage drop equals the sum of the individual voltage drops.


Current in a Series Circuit:

It = I1 = I2 = I3 ....

where
      It current in the series circuit
      I1, I2, .... currents through each resistor which are the same as the total current

Rule: There is only one path for current to flow in a series circuit, therefore the same current flows everywhere in the circuit and is always the same as the total current.


Ohms Law for Parallel Circuits:

Resistance in Parallel:

There are two formulas.

  1. If only two resistors are in parallel, use the following formula:
                         R1 × R2
              RT = ---------
                         R1 + R2
    
  2. If more than two resistors, use the following formula:
                                   1
              RT = ----------------------- ......
                        1               1             1
                      ----  +   ----  +  ----
                        R1             R2           R3
    

Note: The total resistance in parallel is always less than the value of the smallest resistor.


Voltage in a Parallel Circuit:

                  ET = E1 = E2 .... = E N

Note: Voltage is common to all elements in a parallel circuit.


Current in a Parallel Circuit:

                 IT = I1 + I2 + ..... + IN

Note: the total current is the sum of all the individual currents flowing in all of the various branches of the parallel circuit.


Power:


                       P = E × I

                       P = I2 × R

                              E2
                       P = ----
                              R

Where:
      P = power in Watts
      E = voltage in Volts
      I = current in Amperes


Inductors:

Inductors in Series:

               LT = L1 + L2 + .... + LN

Note: same formula as resistors in series


Inductors in Parallel:

                                          1
               LT = ----------------------
                            1        1                1
                          --- + --- + .... + ---
                           L1       L2               LN

Note: same formula as resistors in parallel.


Capacitors:

Capacitors in Parallel:

               CT = C1 + C2 + .... + CN		

Note: same formula as resistors in series.


Capacitors in Series:
	
                                          1
               CT = ----------------------
                            1        1                 1
                          --- + --- + .... + ---
                           C1       C2              CN	

Note: same formula as resistors in parallel.


Reactance:

Inductive Reactance:
	
               XL = 2 × PI × f × L

Where:
      X = inductive reactance in ohms
      2 × PI = 6.28
      f = frequency in hertz
      L = inductance in henries


Capacitive Reactance:
	
                                 1
              XC = -----------
                        2 × PI × f × C

Where:
      X = capacitive reactance in ohms
      2 × PI = 6.28
      f = frequency in hertz
      C = capacitance in farads

Resonance:

	
                                      1
              fR = -----------------
                     2 × PI × SQRT (L × C)

Where:
      f = resonance frequency
      2 PI = 6.28
      L = inductance in henrys
      C = capacitance in farads
      SQRT is short for Square Root


Wavelength:

	
                                        c
              Wavelength = ---
                                        f

                      Wavelength
              c = -----------
                              f

Where:
      Wavelength is in metres
      f = frequency in Hertz
      c = speed of light (300 000 000 metres/second)

This can be simplified if we consider frequency in megahertz:

	
                            300
              f = -----------
                      Wavelength

                                        300
              Wavelength = -----
                                           f

Where:
      Wavelength is in metres
      f = frequency in Hertz
      c = speed of light (300 000 000 metres/second)

Remember: this is for a full wavelength. Divide by two for a half wavelength.


Frequency and Period Relationships:

	
                                      1
              frequency = -----
	                            time
	
                           1
                   f = ---	
                           t

                                   1
              time = ----------
                            frequency

                           1
                   t = ---
                           f

Where:
      t is the time, called period in this case
      f is the frequency

Example: what is the frequency of a waveform having a period of 0.001 seconds?

                  1
             f = ---
                  t

                    1
             f = -------
                  0.001 (sec)

             f = 1 000 (Hz)

Example: what is the period of a signal of 500 Hz?

                  1
             t = ---
                  f

                   1
             t = -----
                  500  (Hz)

             t = 0.002 (seconds)

(this is the time it takes for 1 cycle to occur.)