How to Calculate the Voltage Across a Resistor

Learn about circuits. Visualize an electrical circuit in the following way: imagine pouring a bag of corn kernels into a bowl. Each kernel represents an electron, and the flow of kernels into the bowl symbolizes an electric current. When discussing current, you describe it by stating how many electrons are moving per second.

Think about electric charge. Electrons carry a "negative" charge. This means they are attracted to (or move toward) positively charged objects and repel (or move away from) negatively charged objects. Since they are all negative, electrons constantly repel each other, spreading out whenever possible.

Understand voltage. Voltage is the difference in electric charge between two points. The greater the charge difference, the stronger the attraction between the two ends. Here’s an example using a typical battery:

• In a battery, a chemical reaction occurs, and electrons accumulate. These electrons move toward the negative terminal, while the positive terminal remains nearly empty (they are called the cathode and anode). The longer this process continues, the greater the voltage between the two terminals.
• When a wire connects the negative and positive terminals, the electrons at the negative terminal suddenly have a path to follow. They rush toward the positive terminal, creating an electric current. The higher the voltage, the more electrons move toward the positive terminal each second.

Understand the concept of resistance. Resistance does exactly what its name suggests. The higher the resistance of an object, the harder it is for electrons to move through it. It slows down the current because fewer electrons can pass through each second.

• Resistance is anything in a circuit that adds resistance to the flow. You can buy an actual "resistor" from an electronics store, but in circuit problems, resistance is often represented by a light bulb or any other resistive component.

Remember Ohm’s Law. There is a very simple relationship between current, voltage, and resistance. Write it down or memorize it—you’ll use it frequently when solving circuit problems:

• Current = Voltage divided by Resistance
• It is often written as: I = ^V / _R
• Think about what happens when you increase V (voltage) or R (resistance). Does it align with what you’ve learned in the explanations above?

Understand what a series circuit is. A series circuit is easy to identify. It consists of a single loop where all components are connected in a line. The current flows through the entire loop, passing through each resistor or component one after another.

• Current remains the same at every point in the circuit.
• When calculating voltage, the position of the resistor in the circuit doesn’t matter. You can move or rearrange the resistors, and the voltage across each resistor will remain unchanged.
• Consider an example circuit with three resistors in series: R₁, R₂, and R₃. This circuit is powered by a 12V battery. We will find the voltage across each resistor.

Calculate the total resistance of the circuit. Add up all the resistance values in the circuit. The result is the total resistance of the series circuit.

• For example, three resistors R₁, R₂, and R₃ have resistances of 2 Ω (ohms), 3 Ω, and 5 Ω, respectively. The total resistance is 2 + 3 + 5 = 10 ohms.

Find the current. Use Ohm’s Law to determine the total current in the circuit. Remember, in a series circuit, the current is the same at every point. Once calculated, this current can be used for all further calculations.

• Ohm’s Law states that current I = ^V / _R. The total voltage is 12 volts, and the total resistance is 10 ohms. The answer is I = ¹² / ₁₀ = 1.2 amps.

Rearrange Ohm’s Law to solve for voltage. Using basic algebra, you can rearrange Ohm’s Law to find voltage instead of current:

• I = ^V / _R
• IR = ^VR / _R
• IR = V
• V = IR

Calculate the voltage across each resistor. We know the resistance values, the current, and the equation. Now, plug in the numbers and solve. For the example problem:

• Voltage across R₁ = V₁ = (1.2A)(2Ω) = 2.4V.
• Voltage across R₂ = V₂ = (1.2A)(3Ω) = 3.6V.
• Voltage across R₃ = V₃ = (1.2A)(5Ω) = 6.0V.

Verify your answer. In a series circuit, the total voltage across all resistors must equal the total circuit voltage. Add up all the voltages you calculated and check if they sum to the total circuit voltage. If not, go back and identify the error.

• In our example: 2.4 + 3.6 + 6.0 = 12V, which matches the total circuit voltage.
• If the sum is slightly lower (e.g., 11.97 instead of 12), you likely rounded numbers somewhere. Your answer is still correct.
• Remember, voltage measures the difference in charge, or the number of electrons. Imagine counting the electrons as you move along the circuit. If counted correctly, you’ll end up with the total charge present in the electrons from start to finish.

Understand what a parallel circuit is. Imagine a wire connected to a battery, splitting into two separate wires. These wires run parallel to each other and then reconnect before reaching the other end of the battery. If there’s a resistor on the left wire and another on the right wire, those resistors are connected "in parallel."

• Parallel circuits can have any number of branches. This explanation holds true even if the circuit splits into a hundred wires and then reconnects.

Think about how current flows in the circuit. In a parallel circuit, current flows through every available path. It travels through the left wire, passes the left resistor, and reaches the other end. Simultaneously, it flows through the right wire, passes the right resistor, and reaches the other end. No part of the current flows backward or through both parallel resistors.

Use the total circuit voltage to find the voltage across each resistor. Once you know the total circuit voltage, finding the voltage across each resistor becomes surprisingly simple. Each parallel branch has the same voltage as the total circuit voltage. Consider a circuit with two parallel resistors powered by a 6V battery. The voltage across the left resistor is 6V, and the voltage across the right resistor is also 6V. The resistance values don’t matter. To understand why, revisit the series circuit concept:

• Recall that in a series circuit, the total voltage equals the sum of the voltage drops across each resistor.
• Think of each parallel path as a series circuit. The same logic applies: adding the voltages across all resistors in a path will give you the total circuit voltage.
• Since current flows through only one resistor in each path, the voltage across that resistor must equal the total voltage.

Calculate the total current in the circuit. If the problem doesn’t provide the total circuit voltage, you’ll need to complete a few additional steps. Start by determining the current flowing through the circuit. In a parallel circuit, the total current is the sum of the currents flowing through each parallel branch.

• Mathematically: I_total = I₁ + I₂ + I₃...
• If this is confusing, imagine a water pipe splitting into two. The total water flow is simply the sum of the water flowing through each pipe.

Calculate the total resistance of the circuit. In a parallel circuit, resistors are less effective because they only impede the current flowing through their specific branch. In fact, the more branches there are, the easier it is for current to find a path to the other end. To find the total resistance, solve the following equation for R_total:

• ¹ / _Rtotal = ¹ / _R1 + ¹ / _R2 + ¹ / _R3 ...
• For example, a circuit with resistors of 2 ohms and 4 ohms in parallel. ¹ / _Rtotal = 1/2 + 1/4 = 3/4 → 1 = (3/4)R_total → R_total = 1/(3/4) = 4/3 = ~1.33 ohms.

Find the voltage using the results. Remember, once you determine the total circuit voltage, you’ve also found the voltage across each parallel branch. Use Ohm’s Law to calculate the total voltage. For example:

• Consider a circuit with a current of 5 amps. The total resistance is 1.33 ohms.
• According to Ohm’s Law: I = V / R, so: V = IR.
• V = (5A)(1.33Ω) = 6.65V.