How to Solve a Parallel Circuit

Understanding parallel circuits on paper can help you manage the real thing.

Parallel circuits provide multiple pathways for an electrical current. To solve for a simple parallel circuit, you'll need to know parallel circuit laws that pertain to the circuit's voltage, current/amperage and resistance values. These values are calculated from the circuit's resistive loads (e.g., fuses, bulbs). The values of at least two factors can enable you to calculate for all remaining values. You'll learn how these laws apply through a three-load parallel circuit example.

Things You'll Need

• Graph paper
• Pencil

Instructions

Voltage Values

1. The total voltage value would help you calculate current and resistance values. If the applied/source voltage (i.e. a battery) is 12 volts, then each load's voltage value and the total voltage value is 12V. This is referred to as Kirchhoff's voltage law in parallel circuits.

2. Voltage is signified by E. Sub 1, 2, and 3 are your individual resistive loads.

3. Write your first column like so:

   ETotal = 12V

   E1 = 12V

   E2 = 12V

   E3 = 12V

Resistor Values

1. Resistive load values are often symbolized by Ω (ohm) in circuit diagrams.

2. Create a new column for resistance values signified by R:

   RTotal = XΩ

   R1 = 3Ω

   R2 = 6Ω

   R3 = 4Ω

3. In a moment, you'll learn to solve for RTotal, as there are multiple ways to calculate its value.

Current/Amperage Values

1. Kirchhoff's current law states that a parallel circuit's total current flow equals the sum of each load's current value. Current is labeled as I. Your circuit has a total value of 9 amps (A).

2. Write down on a third column:

   ITotal = 9A

   I1 = 4A

   I2 = 2A

   I3 = X

3. Considering Kirchhoff's law, the current value for the third load would be 3A. Therefore: I3 = 3A.

Solving the Circuit

1. So you should have:

   ETotal = 12V RTotal = XΩ ITotal = 9A

   E1 = 12V R1 = 3Ω I1 = 4A

   E2 = 12V R2 = 6Ω I2 = 2A

   E3 = 12V R3 = 4Ω I3 = 3A

2. The remaining value to solve would be RTotal. Parallel circuit laws state that the total resistance in a parallel circuit should be less than the smallest load value, 3Ω.

3. Ohm's law states that the resistance and voltage values are linked. The voltage of each load can be divided by the resistance values to get the current values, and vice versa. Therefore: 12V ÷ 9A = 1.33Ω (RTotal). The total really is less than the lowest resistive value, 3Ω.

4. To check your work, you can solve for RTotal using the "reciprocal formula method."

   1 1 1 24

   RTotal = ___________ = _________ = _________ = ____ = 1.33

   1 + 1 + 1 8 + 4 + 6 18 18

   _ _ _ ________ ___

   3 6 4 24 24

Tips & Warnings

• Create a chart on your graph paper that provides easy-to-use formulas, such as:

• E ÷ I = R

• I X R = E

• To solve for wattage (P) values: P = E X I (Watt's aw)

• Remember that no matter how complex a parallel circuit is, discovering the voltage value for one load is the same value for all loads and the circuit total.

• Try creating a new circuit with missing values and follow the parallel circuit laws to solve for them.

References

• "Principles of Electricity and Electronics for the Automotive Technician"; Norm Chapman; 2010
• Boston University Physics: Current Resistance