Parallel circuit problems can be solved easily if you understand the basic formulas and principles of parallel circuits. If 2 or more obstacles are connected next to each other, the electric current can "choose" a path (just like a car tends to change lanes and drive side by side if a 1 lane road splits into 2 lanes). After studying this article, you will be able to calculate the value of voltage, current, and resistance for 2 or more resistors connected in parallel.
Basic Formula
- Total resistance formula RT parallel circuit: 1/RT = 1/R1 + 1/R2 + 1/R3 + …
- The value of the electric voltage in each branch of a parallel circuit is always the same: VT = V1 = V2 = V3 = …
- Value of total electric current IT = I1 + I2 + I3 + …
- Ohm's Law Formula: V = IR
Step
Part 1 of 3: Understanding Parallel Circuits
Step 1. Identify parallel circuits
A parallel circuit has 2 or more branches all of which originate from point A and go to point B. A single stream of electrons splits into many branches and then rejoins. Most parallel circuit problems ask the value of the total voltage, resistance, or electric current in the circuit (from point A to point B).
Components that are “assembled in parallel” are each located on a separate branch
Step 2. Understand resistance and electric current in parallel circuits
Imagine a freeway that has multiple lanes and toll booths in each lane slowing down vehicular traffic. Creating a new lane provides an additional lane for cars so that traffic flows more smoothly even though a toll booth is also built in the new lane. So, just like in a parallel circuit, adding a new branch provides a new path for electric current. Regardless of the amount of resistance in the new branch, the total resistance decreases and the total amperage increases.
Step 3. Add up the amperage of each branch to find the total amperage
If the amperage in each branch is known, just add it up to get the total amperage. The total electric current is the amount of electric current that flows through the circuit after all the branches are back together. The formula for total electric current: IT = I1 + I2 + I3 + …
Step 4. Calculate the total resistance value
To find out the total resistance value RT parallel circuit, use the equation 1/RT = 1/R1 + 1/R2 + 1/R3 + … Each R on the right side of the equation represents the resistance value in 1 branch of a parallel circuit.
- Example: a circuit has 2 resistors connected in parallel, each with a value of 4Ω. 1/RT = 1/4Ω + 1/4Ω → 1/RT = 1/2Ω → RT = 2Ω. In other words, 2 branches that have the same resistance are twice as easy to traverse than 1 branch alone.
- If one branch has no resistance (0Ω), all electric current will pass through that branch so the total resistance value = 0.
Step 5. Understand what voltage is
Voltage is the difference in electric potential between 2 points. Since it compares 2 points instead of measuring the flow path, the voltage value remains the same in any branch. VT = V1 = V2 = V3 = …
Step 6. Use Ohm's Law
Ohm's law describes the relationship between voltage V, current I, and resistance R: V = IR. If two of the three values are known, use this formula to find the third value.
Make sure each value comes from the same part of the series. In addition to finding the value in one branch (V = I1R1), Ohm's Law can also be used to calculate the total circuit value (V = ITRT).
Part 2 of 3: Sample Questions
Step 1. Make a table to record the count
If a parallel circuit problem asks for more than one value, the table helps you organize the information. The following is an example of a parallel circuit table with 3 branches. Branches are often written as R followed by a number written in small and slightly downwards.
| R1 | R2 | R3 | Total | Unit | |
|---|---|---|---|---|---|
| V | volt | ||||
| I | ampere | ||||
| R | ohm |
Step 2. Fill in the known values
For example, a parallel circuit uses a 12 volt battery. This circuit has 3 parallel branches, each with resistance of 2Ω, 4Ω, and 9Ω. Write in the table all the known values:
| R1 | R2 | R3 | Total | Unit | |
|---|---|---|---|---|---|
| V | Step 12. | volt | |||
| I | ampere | ||||
| R | Step 2. | Step 4. | Step 9. | ohm |
Step 3. Copy the mains voltage values in each branch
Remember, the value of the voltage across the entire circuit is the same as the value of the voltage across each branch of a parallel circuit.
| R1 | R2 | R3 | Total | Unit | |
|---|---|---|---|---|---|
| V | Step 12. | Step 12. | Step 12. | Step 12. | volt |
| I | ampere | ||||
| R | 2 | 4 | 9 | ohm |
Step 4. Use the Ohm's Law formula to find the amperage of each branch
Each column of the table consists of voltage, current, and resistance. That is, an unknown value can always be found as long as two other values in the same column are known. Remember, Ohm's Law formula is V = IR. The unknown value in our example is electric current. So, the formula can be changed to I = V/R
| R1 | R2 | R3 | Total | Unit | |
|---|---|---|---|---|---|
| V | 12 | 12 | 12 | 12 | volt |
| I | 12/2 = 6 | 12/4 = 3 | 12/9 = ~1, 33 | ampere | |
| R | 2 | 4 | 9 | ohm |
Step 5. Calculate the total electric current
The total electric current is easy to find because it is the sum of the currents of each branch.
| R1 | R2 | R3 | Total | Unit | |
|---|---|---|---|---|---|
| V | 12 | 12 | 12 | 12 | volt |
| I | 6 | 3 | 1, 33 | 6 + 3 + 1, 33 = 10, 33 | ampere |
| R | 2 | 4 | 9 | ohm |
Step 6. Calculate the total resistance
The total resistance can be calculated in two ways. The resistance value line can be used to calculate the total resistance with the equation 1/RT = 1/R1 + 1/R2 + 1/R3. However, the total resistance is often easier to calculate with the Ohm's Law formula which uses the total V and I total values. To calculate resistance, change Ohm's Law formula to R = V/I
| R1 | R2 | R3 | Total | Unit | |
|---|---|---|---|---|---|
| V | 12 | 12 | 12 | 12 | volt |
| I | 6 | 3 | 1, 33 | 10, 33 | ampere |
| R | 2 | 4 | 9 | 12 / 10, 33 = ~1.17 | ohm |
Part 3 of 3: Problem Variations
Step 1. Calculate the electric power
Just like in other circuits, electric power can be calculated by the equation P = IV. If the power in each branch has been calculated, the total power PT equal to the sum of the power of each branch (P1 + P2 + P3 + …).
Step 2. Calculate the total resistance of a two-prong parallel circuit
If a parallel circuit has only two resistances, the formula for total resistance can be simplified to:
RT = R1R2 / (R1 + R2)
Step 3. Calculate the total resistance if the values of all resistances are the same
If all the resistances in a parallel circuit have the same value, the formula for total resistance becomes much simpler: RT = R1 / N. N is the number of resistances in the circuit.
Example: two equal value resistors connected in parallel provide the total resistance of one resistance. Eight equal value barriers provide the total resistance of one resistance
Step 4. Calculate the electric current in the parallel circuit branch without using voltage
An equation known as Kirchhoff's Current Law allows the value of the amperage of each branch to be found even if the circuit voltage is unknown. However, the resistance of each branch and the total current of the circuit must be known.
- Parallel circuit with 2 resistances: I1 = ITR2 / (R1 + R2)
- Parallel circuit with more than 2 resistances: to calculate I1, find the total resistance of all the resistances except R1. Use the parallel circuit resistance formula. Next, use the formula above, with your answer written as R2.
Tips
- If you are working on a mixed circuit (series-parallel) problem, calculate the parallel part first. Next, you just need to calculate the part of the series, which is much easier.
- In a parallel circuit, the voltage is the same across all resistances.
- If you don't have a calculator, the total resistance in some circuits can be difficult to calculate using the R. value1, R2, etc. If this is the case, use the Ohm's Law formula to calculate the amperage of each branch.
- Ohm's Law formula can also be written E = IR or V = AR; different symbols, but the meaning is the same.
- Total resistance is also known as "equivalent resistance".
