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Tristan’s Guide to:
Solving Parallel Circuits.
Version: 1.0
Written in 2006
Written By: Tristan Miller
[email protected]
Parallel Circuits.
Parallel Circuits are a little bit more complicated than a Series Circuit.
The word Parallel basically means Side by Side, or beside one another.
Below is a Parallel circuit.
You can see that the tops of the resistors are connected together, and the bottoms of the
resistors are connected together. This means that the resistors are beside each other, and
in parallel.
This is How Electrons flow in a Parallel Circuit.
Electrons leave the positive
side of the battery, and flow
through the wire to point A.
The electrons split up, some
of the current travels to the
Left, into R1. And some
current travels to the Right,
into R2.
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Once the electrons flow
through the two resistors,
they go through the wires
to point B.
The electrons combine into
the same wire at point B, and
then flow back into the
negative side of the battery.
The Voltage across each resistor in a Parallel
Circuit is the same across each resistor in the
circuit, because each side of the resistors are
connected to the same points in the circuit.
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Calculating the Total Resistance of a Parallel Circuit.
To calculate the total resistance of a parallel circuit, were going to use the formula below:
1
1
1
------ = ------ + -----RT
R1
R2
This can be modified into the equation:
1
----------------1
1
RT = ------ + -----R1
R2
An even easier way is:
RT = 1 ÷ ( (1÷R1) + (1÷R2) )
This form can easily be entered into a calculator!
But be careful, make sure you use the Brackets,
and make sure they are in the right spot.
R1 is 200 Ohms.
R2 is 50 Ohms.
Let’s enter those values into our formula.
RT = 1 ÷ ( (1÷R1) + (1÷R2) )
RT = 1 ÷ ( (1÷200 Ohms) + (1÷50 Ohms) )
RT = 1 ÷ ( (0.005) + ( 0.02) )
RT =1 ÷ (0.025)
RT = 40 Ohms
Therefore; the Total Resistance of the circuit is 40 Ohms.
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Calculating a Missing Resistor Value.
Here’s a circuit with 3 resistors in parallel.
RT is 200 Ohms
R1 is 600 Ohms
R3 is 1.2 Kilo Ohms, or 1200 Ohms.
R2 is Unknown.
Because we know the values of RT, R1 and R3, we can calculate the value of
the missing resistor, R2.
This is the formula to calculate RT.
RT = 1 ÷ ( (1÷R1) + (1÷R2) + (1÷R3) )
We can re-arrange it, so that we have R2 alone on the left side of the equals
sign. It will look like this;
R2 = 1 ÷ ( (1÷RT) – (1÷R1) – (1÷R3) )
Enter in the known values, and solve for R2.
R2 = 1 ÷ ( (1÷200) – (1÷600) – (1÷1200) )
R2 = 1 ÷ ( (0.005) – (0.001666) – (0.000833) )
R2 = 1 ÷ ( (0.003334) – (0.000833) )
R2 = 1 ÷ (0.002501)
R2 = 400 Ohms.
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Calculating Current in a Parallel Circuit.
Calculating the Total Current is the same as the calculation for a Series Circuit.
IT = E ÷ RT
Let’s use this formula for this circuit below:
R1 is 200 Ohms.
R2 is 350 Ohms.
E1 is 9 Volts
IT is Unknown.
We already calculated the Total Resistance of this circuit on the last page, it is 40 Ohms.
We now fill the values that we know, into the formula, and solve for the Total Current.
IT = E ÷ RT
IT = 9 Volts ÷ 40 Ohms
IT = 0.225 A or: IT = 225mA
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Calculating a Missing Resistance with the Total Current.
The total current flows through the wire from the positive side of the battery, to
the tops of the two resistors. At this point, the current slips up, and a part of it
travels through R1, and the other part of the current goes through R2.
We want to calculate how much current goes through R1, and how much goes
through R2.
We’ll use this formula, to calculate the amount of current that goes through R1.
I1 = ( R2 ÷ ( R1 + R2 ) ) * IT
We know the values from the past few pages, so we can enter them into the
formula.
I1 = ( 50 Ohms ÷ ( 200 Ohms + 50 Ohms ) ) * 0.225 Amps
I1 = ( 50 Ohms ÷ 250 Ohms ) * 0.225 Amps
I1 = 0.2 * 0.225 Amps
I1 = 0.045 Amps. Or: I1 = 45 mA.
Therefore the current that flows through R1, is 45 Milliamps.
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Calculating Current in one Resistor with the Voltage.
If you’re given the Voltage in the circuit, you can easily find the current of one
resistor with the formula:
Ix = E1 ÷ Rx
Where ‘x’ is the resistor you are solving for.
Let’s find the current in R2.
We’ll solve it like this:
I2 = E1 ÷ R2
I2 = 9 Volts ÷ 50 Ohms.
I2 = 0.18 Amps or: I2 = 180mA
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