Resistors in Series Page 2
Equivalent Resistance
It turns out that when two resistors are hooked up in series, they present a combined resistance that is equal to their two values added together.
When you see two resistors in series, you can add the values together and replace them with a single resistor. The new resistors value is the sum of the previous two resistors.
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Original Circuit
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New Circuit
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Resistance Total = Resistor 1 + Resistor 2
This is handy if we need a value of resistance that we do not happen to have on hand at the time. Lets say we need 100 ohms of resistance, but can not find a 100 ohm resistor. We can instead use an 80 ohm resistor and a 20 ohm resistor in series since 80 + 20 = 100.
Circuit Reduction of Resistors
When analyzing circuits it is usually easier to reduce the circuit to a simpler circuit in order to to make the math easier. The reduced circuit is mathematically identical to the original circuit. You then use the reduced circuit to answer any questions you have about the original circuit. When you encounter two resistors in series, you can reduce them to one resistor by adding their values together and replacing them with a new resistor that has the value you obtained.
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Original Circuit
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New Circuit
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Resistance Total = 100
In the left schematic above we have two resistors in series. In the right picture we have reduced them to a single, equivalent resistor. Now we can use Ohms Law to figure out how much current is flowing through both circuits, since they are mathematically identical.
Lets start with Ohms Law in its standard form.
A more useful form for this problem is when it is already solved for I (current).
We know that V (volts) is 10, and R (resistance) is 100. Plugging these numbers in to Ohms Law, we get:
I = V / R
I = 10 / 100
I = 0.10 Amps of Current
Now that we know that 0.10 Amps of current are flowing through the circuit, we can go back to our original circuit and label I (current) with the new value.
By using circuit reduction of resistors we have made the math of solving this circuit much easier.
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