How to Calculate the Voltage at the Heads of a Resistor

2024 Author: Samantha Chapman | [email protected]. Last modified: 2024-01-15 13:47

In order to calculate the electrical voltage present across a resistor, you must first identify the type of circuit to be studied. If you need to acquire the basic concepts related to electrical circuits, or if you simply want to refresh your school notions, start reading the article from the first section. If not, you can proceed directly to the section dedicated to analyzing the type of circuit in question.

Steps

Part 1 of 3: Basic Concepts of Electrical Circuits

Step 1. The electric current

Think of this physical size using the following metaphor: imagine pouring corn kernels into a large bowl; each grain represents an electron and the flow of all the grains that fall inside the container represents the electric current. In our example we are talking about flow, that is, the number of corn kernels that enter the bowl every second. In the case of electric current, this is the amount of electrons per second that pass through an electrical circuit. Current is measured in ampere (symbol A).

Step 2. Understand the meaning of electric charge

Electrons are negatively charged subatomic particles. This means that positively charged elements are attracted (or flow towards), while elements with the same negative charge are repelled (or flow away from). Since electrons are all negatively charged they tend to repel each other by moving wherever possible.

Step 3. Understand the meaning of electrical voltage

Voltage is a physical quantity that measures the difference in charge or potential present between two points. The greater this difference, the greater the force with which the two points attract each other. Here is an example involving a classic stack.

• Chemical reactions take place inside a common battery that generate a lot of electrons. The electrons tend to remain close to the negative pole of the battery, while the positive pole is practically discharged, that is, it has no positive charges (a battery is characterized by two points: the positive pole or terminal and the negative pole or terminal). The more the chemical process inside the battery continues, the greater the potential difference present between its poles.
• When you connect an electric cable to the two poles of the battery, the electrons present in the negative terminal finally have a point to move towards. They will then be quickly attracted to the positive pole creating a flow of electrical charges, that is, a current. The higher the voltage, the greater the amount of electrons per second flowing from the negative to the positive pole of the battery.

Step 4. Understand the meaning of electrical resistance

This physical quantity is exactly what it seems, that is the opposition - or indeed the resistance - generated by an element to the passage of the flow of electrons, that is, of the electric current. The greater the resistance of an element, the more difficult it will be for electrons to pass through it. This means that the electric current will be lower because the number of electric charges per second that will be able to cross the element in question will be lower.

A resistor is any element in an electrical circuit that has a resistance. You can purchase a "resistor" at any electronics store, but when studying educational electrical circuits, these elements could be represented by a light bulb or any other element that offers resistance

Step 5. Learn Ohm's Law

This law describes the simple relationship that links the three physical quantities involved: current, voltage and resistance. Write it down or memorize it, as you will use it very often to troubleshoot electrical circuit problems, at school or at work:

• The current is given by the relationship between the voltage and the resistance.
• It is usually indicated by the following formula: I = ^V. / _R.
• Now that you know the relationship between the three forces at play, try to imagine what happens if the voltage (V) or the resistance (R) is increased. Does your answer agree with what you have learned in this section?

Part 2 of 3: Calculating the Voltage Across a Resistor (Series Circuit)

Step 1. Understand the meaning of series circuit

This type of connection is easy to identify: it is in fact a simple circuit in which each component is connected in sequence. The current flows through the circuit, passing through all the resistors or components present one at a time, in the exact order in which they are found.

• In this case the current it is always the same in every point of the circuit.
• When calculating the voltage, it does not matter where the individual resistors are connected. In fact, you could very well move them along the circuit as you wish, without the voltage present at each end being affected by this change.
• Let's take as an example an electrical circuit in which there are three resistors connected in series: R.₁, R₂ and R₃. The circuit is powered by a 12 V battery. We must calculate the voltage present across each resistor.

Step 2. Calculate the total resistance

In the case of resistors connected in series, the total resistance is given by the sum of the individual resistors. We then proceed as follows:

Let's assume for example that the three resistors R₁, R₂ and R₃ have the following values 2 Ω (ohm), 3 Ω and 5 Ω respectively. In this case the total resistance will therefore be equal to 2 + 3 + 5 = 10 Ω.

Step 3. Calculate the current

To calculate the total current in the circuit, you can use Ohm's law. Remember that in a series connected circuit, the current is always the same at every point. After calculating the current in this way, we can use it for all subsequent calculations.

Ohm's law states that the current I = ^V. / _R.. We know that the voltage present in the circuit is 12 V and that the total resistance is 10 Ω. The answer to our problem will therefore be I = ¹² / ₁₀ = 1, 2 A.

Step 4. Use Ohm's Law to calculate voltage

Applying some simple algebraic rules we can find the inverse formula of Ohm's law to calculate the voltage starting from current and resistance:

• I = ^V. / _R.
• I * R = ^V.R / _R.
• I * R = V
• V = I * R

Step 5. Calculate the voltage across each resistor

We know the value of the resistance and the current and also of the relationship that binds them, so we just have to replace the variables with the values of our example. Below we have the solution to our problem using the data in our possession:

• Voltage across resistor R.₁ = V₁ = (1, 2 A) * (2 Ω) = 2, 4 V.
• Voltage across resistor R.₂ = V₂ = (1, 2 A) * (3 Ω) = 3, 6 V.
• Voltage across resistor R.₃ = V₃ = (1, 2 A) * (5 Ω) = 6 V.

Step 6. Check your calculations

In a series circuit the total sum of the individual voltages present across the resistors must be equal to the total voltage supplied to the circuit. Add the individual voltages to verify that the result is equal to the voltage supplied to the entire circuit. If not, check all the calculations to find out where the error is.

• In our example: 2, 4 + 3, 6 + 6 = 12 V, exactly the total voltage supplied to the circuit.
• In the event that the two data should differ slightly, for example 11, 97 V instead of 12 V, the error will most likely derive from the rounding performed during the various steps. Your solution will still be correct.
• Remember that voltage measures the potential difference across an element, in other words the number of electrons. Imagine being able to count the number of electrons you encounter while traveling the circuit; counting them correctly, at the end of the journey you will have exactly the same number of electrons present at the beginning.

Part 3 of 3: Calculating the Voltage Across a Resistor (Parallel Circuit)

Step 1. Understand the meaning of parallel circuit

Imagine you have an electrical cable whose end is connected to one pole of a battery, while the other is split into two other separate cables. The two new cables run parallel to each other and then rejoin again before reaching the second pole of the same battery. By inserting a resistor in each branch of the circuit, the two components will be connected to each other "in parallel".

Within an electrical circuit there is no limit to the number of parallel connections that can be had. The concepts and formulas in this section can also be applied to circuits that have hundreds of parallel connections

Step 2. Imagine the flow of current

Within a parallel circuit, the current flows within each branch or path available. In our example, the current will go through both the right and the left cable (including the resistor) at the same time, then reaching the other end. No current in a parallel circuit can travel through a resistor twice or flow inside it in reverse.

Step 3. To identify the voltage across each resistor we use the total voltage applied to the circuit

Knowing this information, getting the solution of our problem is really simple. Within the circuit, each "branch" connected in parallel has the same voltage applied to the entire circuit. For example, if our circuit where there are two resistors in parallel is powered by a 6 V battery, it means that the resistor on the left branch will have a voltage of 6 V, as well as the one on the right branch. This concept is always true, regardless of the resistance value involved. To understand the reason for this statement, think again for a moment to the series circuits seen previously:

• Remember that in a series circuit the sum of the voltages present across each resistor is always equal to the total voltage applied to the circuit.
• Now imagine that each "branch" traversed by the current is nothing more than a simple series circuit. Also in this case the concept expressed in the previous step remains true: adding the voltage across the individual resistors, you will get the total voltage as a result.
• In our example, since the current flows through each of the two parallel branches in which there is only one resistor, the voltage applied across the latter must be equal to the total voltage applied to the circuit.

Step 4. Calculate the total current in the circuit

If the problem to be solved does not provide the value of the total voltage applied to the circuit, to arrive at the solution you will need to perform additional calculations. Start by identifying the total current flowing within the circuit. In a parallel circuit, the total current is equal to the sum of the individual currents passing through each of the branches present.

• Here's how to express the concept in mathematical terms:_total = I₁ + I₂ + I₃ + I.
• If you have trouble understanding this concept, imagine you have a water pipe that, at a certain point, is split into two secondary pipes. The total quantity of water will be simply given by the sum of the quantities of water flowing inside each single secondary pipe.

Step 5. Calculate the total resistance of the circuit

Since they can offer resistance only to the portion of current flowing through their branch, in a parallel configuration the resistors do not work efficiently; in fact, the greater the number of parallel branches present in the circuit, the easier it will be for the current to find a path to cross it. To find the total resistance, the following equation must be solved based on R._total:

• ¹ / _{R.total = ¹ / R.1 + ¹ / R.2 + ¹ / R.3}
• Let's take the example of a circuit in which there are 2 resistors in parallel, respectively of 2 and 4 Ω. We will get the following: ¹ / _{R.total = 1/2 + 1/4 = 3/4 → 1 = (3/4) R.total → Rtotal = 1 / (3/4) = 4/3 = ~ 1,33 Ω.}

Step 6. Calculate the voltage from your data

Remember that, once you have identified the total voltage applied to the circuit, you will also have identified the voltage applied to each single branch in parallel. You can find the solution to this question by applying Ohm's law. Here is an example:

• There is a current of 5 A in a circuit. The total resistance is 1.33 Ω.
• Based on Ohm's law we know that I = V / R, so V = I * R.
• V = (5 A) * (1,33 Ω) = 6,65 V.

Advice

• If you have to study an electrical circuit in which there are resistors in series and resistors in parallel, start the analysis by starting with two nearby resistors. Identify their total resistance using the appropriate formulas for the situation, relating to resistors in parallel or in series; now you can consider the pair of resistors as a single element. Continue studying the circuit using this method until you have reduced it to a simple set of resistors configured in series or in parallel.
• The voltage across a resistor is often referred to as a "voltage drop".

• Get the right terminology:

  • Electric circuit: set of electrical elements (resistors, capacitors and inductors) connected to each other by an electric cable in which there is a current.
  • Resistor: electrical component that opposes a certain resistance to the passage of an electric current.
  • Current: ordered flow of electrical charges within a circuit; unit of measurement ampere (symbol A).
  • Voltage: difference in electric potential existing between two points; unit of measurement volts (symbol V).
  • Resistance: physical quantity that measures the tendency of an element to oppose the passage of an electric current; unit of measurement ohm (symbol Ω).