Resistance and Resistors:

        Resistors may be combined in any of three ways: in series,in
parallel, or in series parallel. When resistors are wired in series,
the total circuit resistance increases because each resistor contrebutes
opposition to the circuit's current flow. Therefore if a 10 ohm resistor
is placed in series with another 10 ohm resistor, the total resistance
contributed by the two resistors is 20 ohms. Similarly, if three 10 ohm
resistors are wired in series, the total resistance is 30 ohms. The 
formula for resistors in series is to just add the resistances together.

                Resistance Total= R1 + R2 + R3

        If the resistors all have the same resistance then the voltage
drop across each of the resistors is the same, but if the resistors have
different amounts of resistance, then the voltage drop across each resistor
is different. If you have 3 resistors in series, for example a 4 ohm +
an 8 ohm + a 3 ohm, the total resistance is 15 ohms. If you connect a
30 volt battery to the three resistors in series, the current being equal
to the voltage divided by the resistance I=E/R would be 2 amps. Because
the individual resistors have different values, the amount of voltage across
each resistor differs. Across the 4 ohm resistor, there is a drop of
8 volts (2 amps multiplied by 4 ohms) E=IR. Across the 8 ohm resistor,
there is a drop of 16 volts, and across the 3 ohm resistor a drop of 6 volts
exists. When these individual voltages are added together, they will equal
the total voltage previously calculated of 30 volts, 8+16+6=30 volts.

                current x resistance = voltage
                   2    x      4     =  8   
                   2    x      8     =  16
                   2    x      3     =  6   
                 -----------------------------  
                   2    x      15    =  30

        Total current in this example is 2 amps. Because the resistors are
in series, the amount of current at any point in the circuit is the same.
It must be remembered that current is a measure of the amount of electron
flow past a given point for a certain length of time. This amount would not
change unless the applied pressure (voltage) or the resistance value (Ohms)
changes. Thus, current is always the same through any portion of a given
series circuit, though the voltage across an individual resistor is proportional
to the resistance value. In a series circuit, it is necessary only to solve
for the current through any one of the several resistors to obtain
the current value for the entire circuit.

        While current in any part of a series circuit is the same as in any
other part of the circuit, it must be remembered that the current depends on 
the amount of resistance as well as the voltage. If either the resistance or 
the voltage changes, the current value will also change.

Parallel Resistors:

        Resistors in a parallel circuit arrangement such as two 8 Ohm
resistors in parallel with a 32 volt source. When resistors are in parallel
the voltage source connects directly to each resistor, therfore the total
source voltage is present across each resistor. The total value of resistance
can be found by the formula:

                R total= R1 x R2 divided by R1 + R2

                R total= 8x8/8+8= 64 divided by 16= 4 Ohms

        Thus, when two parallel resistors are equal in value, 
the total resistance is half that of a single resistor. Since the two 
resistors are equal in value, each one will have the same amount of current
flowing through it. Because the two resistors are placed across the power
source, the current divides, and the current through the first resistor is
E/R=32 divided by 8 = 4 amps. Since the second resistor also draws 4 amps
the two parallel resistors draw a total of 8 amps.

        To find the total power consumed by the two resistors, we use the
formula: 
                P = I squared times R= (8x8)4= 64 x 4 = 256 watts

        In many branches of electrical circuits, the values of current are
often in fractional amperes and fractional values are also encountered in
wattages. In consequence, the terms milliamperes and milliwatts are
frequently used.

        A point to remember is that when two or more resistors are in
parallel the total resistance is always less than the value of the lowest
resistance. This rule does not apply to resistors in series since the
addition of resistors increases the total resistance.

        When more than two resistors are in parallel the following formula
must be used:

                R total= the reciprocal of the total of the reciprocals

                R total=                   1
                            ----------------------------------
                              1      1       1       1       1
                             ---  + ----  + ----  + ----  + ----
                              R1     R2      R3      R4      R5
Top of Page