Electrical Circuit Calculations

Individual electrical circuits normally combine one or more resistance or load devices. The design of the electrical circuit will determine which type of circuit is used. There are three basic types of circuits: the series circuit, the parallel circuit, and the series-parallel circuit.

Series Circuit Calculations

A series circuit is a circuit in which a given current begins at the voltage source, passes through each electrical device in a single pathway, before returning to the voltage source. In calculating values for current, voltage, power and resistance, the following rules apply...


RULE #1: Current (Amps)
The current remains the same throughout a series circuit.

RULE #2: Voltage (EMF)
The total voltage of a series circuit equals the total of all of the voltages of the resistors in the circuit added together.

RULE #3: Power (Watts)
The total power of a series circuit equals the total of all of the wattages of the individual resistors in the circuit.

RULE #4: Resistance (Ohms)
The total resistance of a series circuit equals the total all of the resistances added together.

 

Series Circuit Example


The great thing about using the Ohm's Law Ladder is that we can set one up at any point of a series or parallel circuit. In the series circuit above we have set up ladders at each resistor and the totals at the power supply.

In the circuit below our power supply (battery) has a total of 12 watts of power, 12 volts, 1 amp, and 12 ohms of resistance. By applying the four series circuit rules we find that our current (1 amp) is the same everywhere in the circuit. This is due to the fact that all of the electrons (current flow) that leave the power source return back to the source eventually. The sum total of watts, volts, and resistance can be found by finding the totals of each.

 


Resistance: The sum total of a series circuit equals the total all of the resistances added together.

Total Resistance "R" = 12 (2 + 4 +6)


Current remains the same throughout the circuit. Now that we know that there is 1 Amp at the power supply we know that there is 1 Amp everywhere in the circuit. The sum total Volts = 12, and total total Resistance (Ohms) = 12, we can find amps at the power source.

12 Volts / 12 Ohms = 1 Amp


Voltage The total voltage of a series circuit equals the total of all of the voltages of the resistors in the circuit added together.

Total Volts "E" = 12 (2 + 4 +6)


Watts (Power) the total of a series circuit equals the total of all of the wattages of the resistors in the circuit added together.

Total Watts "W" = 12 (2 + 4 +6)

Don't forget...

Parallel Circuit Calculations


A parallel circuit is a circuit in which the current branches out so that only part of the current beginning at the voltage source passes through each resistor. In calculating values for voltage, current, power and ohms, the following rules apply:

RULE #1: Voltage (EMF)
The voltage remains the same throughout a parallel circuit.

RULE #2: Current (Amps)
The total current of a parallel circuit equals the total of all of the currents of the resistors in the circuit added together.

RULE #3: Power (Watts)
The total power of a parallel circuit equals the total of all of the wattages of the resistors in the circuit added together.

RULE #4: Resistance (Ohms)
The total resistance in a parallel circuit must use the following formula due to the fact that the current branches out into each resistor simultaneously.


                                                            1                      
 Total Resistance     =      1                 1                  1   
                                        R1     +       R2     +        R3...

 

Parallel Circuit Example


Let's try the Ohm's Law Ladder on a parallel circuit. We have set up ladders at each resistor (#1, #2, #3), and the totals at the power supply. Notice that all known resistor values have been placed by their respective variables: Total E = 12, R#1 = 2, R#2 = 4, R#3 = 6. Applying the four Parallel circuit rules we find;


VOLTAGE
The voltage remains the same throughout the circuit.


Total Voltage =  12

R#1 Voltage   =  12
R#2 Voltage   =  12
R#3 Voltage   =  12


CURRENT The total current of a parallel circuit equals the total of all of the current of the resistors in the circuit added together.

Total Current = 6 + 3 + 2
Total Current = 11

POWER total of a parallel circuit equals the total of all of the wattages of the resistors in the circuit added together.


Total Watts  =  72 + 36 + 24
Total Watts  =  132


RESISTANCE total of a parallel circuit equals the total of all the voltages divided by the total of all the amperages.


Total Resistance  =      Total Volts_
                                    Total Amps

Total Resistance  = 12 / 11
Total Resistance  = 1.1

That's a lot easier than this old formula...


                                                               1                       
 Total Resistance     =       1           1             1   
                                       2  +       4       +    6

 
 

Series-Parallel Circuits


It is possible to combine series and parallel circuits in order to alter voltages, using series circuits, or currents, using parallel circuits, to meet various load requirements. In solving series-parallel calculations you must first separate the circuit into its series and parallel parts. Each part of the circuit can be solved separately through common resistors.




For example; notice that resistor #3 in the circuit above is common to both parts of the circuit. In calculating the parallel section, all of the parallel circuit rules apply; voltage remains the same throughout the circuit, current, and wattage are additive. Find the total resistance in this part of the problem.


Use this formula...
                                                                          
                             1          
Total R  =      1              1  
                    R1   +     R2

Here’s an alternate formula:
                          
     Total R =   __R3 x   R4__
                            R3 +   R4

Was your answer for total resistance 1.3 ohms ?

If the total resistance for the two parallel resistors is 1.3 ohms, then resistor #3 which is common with the series part of the circuit is carrying 1.3 ohms. Remember, resistor #3 equals the total resistance of the parallel part of the circuit (R#3 + R#4).

Now, calculating the rest of the problem is the same as calculating a series circuit with three resistors. Resistance total for a series circuit is additive.

R Total  =  R#1  +  R#2  +  R#3
R Total  =  1  +  1  +  1.3
R Total  =  3.3 ohms



Series-Parallel Tip: Always start at the resistor farthest away from the power source then work back.