When you know the basic formulas and principles, it is not difficult to solve circuits in parallel. When two or more resistors are connected directly to the power supply, the current flow can "choose" which path to follow (just like cars do when the road splits into two parallel lanes). After reading the instructions in this tutorial, you will be able to find the voltage, current and resistance in a circuit with two or more resistors in parallel.
Memorandum
- The total resistance R.T. for resistors in parallel it is: 1/R.T. = 1/R.1 + 1/R.2 + 1/R.3 + …
- The potential difference across each branch circuit is always the same: V.T. = V1 = V2 = V3 = …
- The total current intensity is equal to: IT. = I1 + I2 + I3 + …
- Ohm's law states that: V = IR.
Steps
Part 1 of 3: Introduction
Step 1. Identify the parallel circuits
In this type of diagram, you can see that the circuit is composed of two or more leads that all start from point A to point B. The same flow of electrons splits to go through different "branches" and, finally, rejoins from the other party. Most problems involving a parallel circuit require you to find the total difference in electrical potential, resistance, or current strength of the circuit (from point A to point B).
The elements "connected in parallel" are all on separate branch circuits
Step 2. Study the resistance and current intensity in parallel circuits
Imagine a ring road with several lanes and with a toll booth in each of them that slows down traffic. If you build another lane, the cars have an additional channeling option and the travel speed increases, even if you had to add another toll booth. Similarly, by adding a new branch circuit to one in parallel, you allow the current to flow along another path. No matter how much resistance this new circuit puts up, the total resistance of the entire circuit decreases and the current intensity increases.
Step 3. Add the current strength of each branch circuit to find the total current
If you know the intensity value of each "branch", then just proceed with a simple sum to find the total: it corresponds to the amount of current that runs through the circuit at the end of all branches. In mathematical terms, we can translate it with: IT. = I1 + I2 + I3 + …
Step 4. Find the total resistance
To calculate the value of R.T. of the whole circuit, you need to solve this equation: 1/R.T. = 1/R.1 + 1/R.2 + 1/R.3 +… Where each R to the right of the equality sign represents the resistance of a branch circuit.
- Consider the example of a circuit with two resistors in parallel, each with a resistance of 4Ω. Therefore: 1/R.T. = 1/ 4Ω + 1/ 4Ω → 1/R.T. = 1/ 2Ω → R.T. = 2Ω. In other words, the flow of electrons, going through the two derivative circuits, encounters half the resistance compared to when it travels only one.
- If a branch had no resistance, then all current would flow through this branch circuit and the total resistance would be 0.
Step 5. Remember what the voltage indicates
Voltage measures the difference in electrical potential between two points, and since it is the result of comparing two static points and not a flow, its value remains the same no matter which branch circuit you are considering. Therefore: VT. = V1 = V2 = V3 = …
Step 6. Find the missing values thanks to Ohm's law
This law describes the relationship between voltage (V), intensity of current (I) and resistance (R): V = IR. If you know two of these quantities, then you can use the formula to calculate the third.
Make sure that each value refers to the same portion of the circuit. You can use Ohm's law to study the whole circuit (V = IT.R.T.) or a single branch (V = I1R.1).
Part 2 of 3: Examples
Step 1. Prepare a chart to track your work
If you are faced with a parallel circuit with several unknown values, then a table helps you organize the information. Here are some examples for studying a parallel circuit with three leads. Remember that branches are often indicated with the letter R followed by a numeral subscript.
| R.1 | R.2 | R.3 | Total | Unit | |
|---|---|---|---|---|---|
| V. | volt | ||||
| THE | ampere | ||||
| R. | ohm |
Step 2. Complete the table by entering the data provided by the problem
For our example, let's assume the circuit is powered by a 12 volt battery. In addition, the circuit has three leads in parallel with resistances of 2Ω, 4Ω and 9Ω. Add this information to the table:
| R.1 | R.2 | R.3 | Total | Unit | |
|---|---|---|---|---|---|
| V. | Step 12. | volt | |||
| THE | ampere | ||||
| R. | Step 2. | Step 4. | Step 9. | ohm |
Step 3. Copy the potential difference value to each branch circuit
Remember that the voltage applied to the entire circuit is equal to that applied to each branch in parallel.
| R.1 | R.2 | R.3 | Total | Unit | |
|---|---|---|---|---|---|
| V. | Step 12. | Step 12. | Step 12. | Step 12. | volt |
| THE | ampere | ||||
| R. | 2 | 4 | 9 | ohm |
Step 4. Use Ohm's Law to find the current strength in each lead
Each column of the table reports the voltage, intensity and resistance. This means you can solve the circuit and find the missing value when you have two data on the same column. If you need a reminder, remember Ohm's Law: V = IR. Given that the missing datum of our problem is the intensity, you can rewrite the formula as: I = V / R.
| R.1 | R.2 | R.3 | Total | Unit | |
|---|---|---|---|---|---|
| V. | 12 | 12 | 12 | 12 | volt |
| THE | 12/2 = 6 | 12/4 = 3 | 12/9 = ~1, 33 | ampere | |
| R. | 2 | 4 | 9 | ohm |
Step 5. Find the total intensity
This step is very simple, as the total current intensity is equal to the sum of the intensity of each lead.
| R.1 | R.2 | R.3 | Total | Unit | |
|---|---|---|---|---|---|
| V. | 12 | 12 | 12 | 12 | volt |
| THE | 6 | 3 | 1, 33 | 6 + 3 + 1, 33 = 10, 33 | ampere |
| R. | 2 | 4 | 9 | ohm |
Step 6. Calculate the total resistance
At this point, you can proceed in two different ways. You can use the resistance row and apply the formula: 1/R.T. = 1/R.1 + 1/R.2 + 1/R.3. Or you can proceed in a simpler way thanks to Ohm's law, using the total values of voltage and current intensity. In this case, you have to rewrite the formula as: R = V / I.
| R.1 | R.2 | R.3 | Total | Unit | |
|---|---|---|---|---|---|
| V. | 12 | 12 | 12 | 12 | volt |
| THE | 6 | 3 | 1, 33 | 10, 33 | ampere |
| R. | 2 | 4 | 9 | 12 / 10, 33 = ~1, 17 | ohm |
Part 3 of 3: Additional Calculations
Step 1. Calculate the power
As in any circuit, the power is: P = IV. If you found the power of each lead, then the total value PT. is equal to the sum of all partial powers (P.1 + P2 + P3 + …).
Step 2. Find the total resistance of a circuit with two leads in parallel
If there are exactly two resistors in parallel, you can simplify the equation as a "product of the sum":
R.T. = R1R.2 / (R1 + R2).
Step 3. Find the total resistance when all resistors are identical
If every resistance in parallel has the same value, then the equation becomes much simpler: R.T. = R1 / N, where N is the number of resistors.
For example, two identical resistors connected in parallel generate a total circuit resistance equal to half of one of them. Eight identical resistors provide a total resistance equal to 1/8 the resistance of just one
Step 4. Calculate the current intensity of each lead without having the voltage data
This equation, called Kirchhoff's law of currents, allows you to solve each branch circuit without knowing the applied potential difference. You need to know the resistance of each branch and the total intensity of the circuit.
- If you have two resistors in parallel:1 = IT.R.2 / (R1 + R2).
- If you have more than two resistors in parallel and you need to solve the circuit to find I.1, then you need to find the combined resistance of all resistors besides R.1. Remember to use the formula for resistors in parallel. At this point, you can use the previous equation by substituting for R.2 the value you just calculated.
Advice
- In a parallel circuit, the same potential difference applies to each resistor.
- If you don't have a calculator, it is not easy for some circuits to find the total resistance from the formula R.1, R2 and so on. In this case, use Ohm's law to find the current strength in each branch circuit.
- If you have to solve mixed circuits in series and in parallel, tackle those in parallel first; eventually you will have a single circuit in series, easier to calculate.
- Ohm's law may have been taught to you as E = IR or V = AR; know that it is the same concept expressed with two different notations.
- Total resistance is also referred to as "equivalent resistance".
