Notice that in the picture to the left, that there are 3 different paths which the water can take. All 3 paths have the same incoming pressure, but the flow of some paths can be more restricted than in others. Parallel circuits in electronics work on the same principle. While there may be multiple paths for the electricity to flow through, the electrical pressure (Voltage) remains the same through all paths.
As you can see from the diagram on the right, there are 4 meters placed in this circuit to measure the current. The first 3, (A _{ 1 } , A _{ 2 } , and A _{ 3 } ) measure only the current flowing through that individual leg of the circuit. The 4th, A _{ T } measures the Total current of the circuit.
If you take the three individual currents, and add them all together, they will equal the total current, measured on the 4th meter. From this we can see that the current in a parallel circuit is additive.
Resistance in a parallel circuit can be quite a bit trickier than in a series circuit. It is found by " Reciprocating the Sum of the Reciprocals ". (huh?)Simple. Taking the reciprocal of a number means dividing "1" by that number. The reciprocal of 2 would be 1 divided by 2 or ½. Most modern calculators have a [1/X] button just for this purpose. So if you take the reciprocals of the values of all of the resistors, which would, of course, give you a bunch of fractions, and add them all up, then reciprocate their sum, you would have the answer. The formula would look something like this:
Confused yet? Good.... let's see if we can clear it all up in lesson 13!
Parallel Circuits  the Plague!
R _{ 1 } = 50 Ω
R _{ 2 } = 200 Ω
A _{ 1 } reads .2 Amps in current ( I=.2 )
Find:
Total Voltage
Total Circuit Resistance
Total Current
And Finally, the Current through A _{ 2 }
Now this isn't as tuff as it first looks. Let's break the problem down. We know according to Ohm's law, that if we know the resistance and current, we can find the voltage.
E _{ R1 } = I _{ R1 } x R _{ 1 } .
E = .2 x 50 = 10
E = 10 Volts.
Now that we know that the voltage for the entire circuit is 10 volts, let's find the total Resistance.
First, we find the reciprocals of the individual resistances:
R _{ 1 } = 50 ohms. 1/50 = .02
R _{ 2 } = 200 ohms. 1/200 = .005
Now we add the two reciprocals together:
.02 + .005 = .025
Finally we take the reciprocal of the sum:
1 / .025 = 40 Ω
So if the Total Voltage of the circuit is 10 Volts, and the Total Resistance = 40 Ω then by using Ohms Law again we can find the total current.
I _{ Total } = E _{ Total } / R _{ Total }
I = 10/40 = ¼ Ampere.
Almost finished now. So far we know:
R _{ 1 } = 50 Ω
R _{ 2 } = 200 Ω
A _{ 1 } reads .2 Amps in current ( I=.2 )
V _{ Total } = 10
R _{ Total } = 40
and
I _{ Total } = ¼
Now we have at least 2 methods by which we can find the current through A _{ 2 } .
We know that the Total current is the sum of all the individual leg currents, so if we subtract the current of A _{ 1 } from the Total current we get this:
I _{ Total }  I _{ 1 } = I _{ 2 } .25  .2 = I _{ 2 } = .05 Amperes.
The other method would be by using Ohms Law. We know the resistance of R _{ 2 } = 200 Ω. We also know that the voltage across R _{ 2 } = 10 Volts. Hence:
10 Volts / 200 Ω = .05 Amperes.
Either way, our final result is A _{ 2 } = .05 Amps
Series and Parallel Resistances  a Summary

To summarize all that we have just learned:
 There are 2 types of circuits.... Series and Parallel.

Series Circuits
 Are connected in a straight line, like a chain.
 All current remains the same throughout the circuit.
 There can be many different voltages in a series circuit, as a voltage drop appears across every resistor.
 The total voltage in a series circuit is equal to the sum of all the individual voltage drops within the circuit.
 The total resistance in a series circuit is equal to the sum of all the individual resistances within the circuit.

The formula for Resistance in Series is:

R
_{
Total
}
= R
_{
1
}
+ R
_{
2
}
+ R
_{
3
}
+ etc...

I
_{
Total
}
= I
_{
1
}
=I
_{
2
}
=I
_{
3
}
etc...

E
_{
Total
}
= E
_{
1
}
+ E
_{
2
}
+ E
_{
3
}
+ etc...

Parallel Circuits
 Are connected allowing multiple paths for current flow.
 All voltage remains the same throughout the circuit.
 There can be many different currents in a parallel circuit, as each leg has the same voltage, but can have a different resistance.
 The total current in a parallel circuit is equal to the sum of all the individual currents on each leg of the circuit.

The formula for Current in Parallel is:

I
_{
RTotal
}
= I
_{
R1
}
+ I
_{
R2
}
+ I
_{
R3
}
+ etc...
 Resistance is found by reciprocating the sum of the reciprocals of the resistance of the individual branches

The formula for Resistance in Parallel is:

1

1 1 1 1 1
 +  +  +  +  +
R _{ 1 } R _{ 2 } R _{ 3 } R _{ 4 } R _{ X... }

E
_{
Total
}
= E
_{
1
}
=E
_{
2
}
=E
_{
3
}
etc...
 Ohm's Law states that there is a relationship which exists between current, resistance, and voltage, such that E = I x R