How to Calculate Series in a Parallel Circuit
Voltage, resistance, and current in an electrical circuit can be calculated using the following simple formula known as Ohm's Law: V=IR, where V is the voltage, I is the current, and R is the resistance. As with any simple algebraic equation of this form, all but one value must be known in order to solve for the final value. Therefore, if we know the resistance and current at any point in an electrical circuit, we can also calculate the voltage at that point. The resistance for resistors that are arrange side-by-side, otherwise known as a series, is calculated by simply adding the individual resistances. For resistors that are arranged in a parallel configuration, resistance is calculated by taking the reciprocal of the summation of the individual reciprocals of the resistors. However, calculating for resistance in a combination series-parallel resistor circuit is a bit more challenging. It can be accomplished using the following analysis technique.
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Instructions
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Calculating Resistance and Current Through a Series-Parallel Circuit
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1
Draw a table to account for all variables in the equation. The table should have three rows with one row labeled V for voltage, another labeled R for resistance, and the last one labeled I for current. Include enough columns to account for every resistor plus one to account for totals. Plug in all known values from the schematic.
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2
Identify which parts of the circuit on the schematic are in a parallel configuration and which are in a series configuration. Reduce these parts down to one equivalent resistor per part by using the procedure for calculating series and parallel resistance discussed in the overview. For example, a component of the circuit with two resistors in a series would be redrawn to one resistor with the value of the summation of the individual resistors.
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3
Add a column to your table for every equivalent resistor you calculate and record the values.
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4
Repeat the procedure outlined in Step 2 and Step 3 until the resistors in the circuit are simplified to one equivalent resistor. Using the equivalent resistance and total voltage, calculate the total current with Ohm's Law. Record the total values on your table.
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5
Redraw the schematic working backwards through the steps you took to reduce the resistors. For example, if the final simplification you made was to combine two resistors in series into one equivalent resistor, redraw the diagram to two resistors in a series.
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6
Calculate the current, resistance, and voltage after each step of expanding the schematic. Use Ohm's Law and your general knowledge for how electrical currents work to accomplish this. Currents that pass through resistors in a series will be equivalent. Therefore, if the first step you take in working backwards is to separate one resistor into two resistors in a series, the current through the resistors will be the same as the total current calculated. If separating an equivalent resistor into two parallel resistors, the voltage through each will be equivalent. Continue this process until you have returned to the original complexity of the schematic and all values are calculated.
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Tips & Warnings
Be sure to draw a separate circuit schematic for every step of reducing the resistors. This will help greatly when working backwards to expand the circuit and calculate all values.
