How to Calculate the Voltage of a Resistor

Understand what is a series circuit. Series circuits are easy to identify. It’s just a coil, with everything lined up in a row. Current moves around the entire coil, passing through each resistor or component that makes up the circuit in turn.

• The current is always the same at every point in the circuit. ^[2]
• When calculating voltage, the position of the resistor in the circuit does not matter. You can take and change the resistor position, the voltage of each resistor will remain the same.
• Consider the example circuit with three resistors in series: R ₁ , R ₂ , and R ₃ . This circuit is powered by a 12V battery. We will find the voltage of each resistor.

Calculate the total resistance of the circuit. Add up all the resistor values in the circuit. The answer obtained is the total resistance of the series circuit.

• For example, the three resistors R ₁ , R ₂ , and R ₃ have resistances of 2 Ω (ohm), 3 , and 5 Ω respectively. The total resistance of the circuit is 2 + 3 + 5 = 10 ohms.

Find the amperage. Use Ohm’s law to find the total current in the circuit. Remember that in series circuits, the amperage is the same everywhere. Once we have calculated the line in this way, we can use it for any calculation.

• Ohm’s law says that amperage I = ^V / _R . The voltage across the circuit is 12 volts, and the total resistance is 10 ohms. The answer is I = ¹² / ₁₀ = 1.2 amp .

Transform Ohm’s law to find the voltage. With basic algebra, we can transform Ohm’s law to find voltage instead of amperage:

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

Calculate the voltage of each resistor. We know the resistance value, we know the amperage and we have the equation. Change numbers and solve. For the example problem, we have:

• Voltage of R ₁ = V ₁ = ( 1.2A )( 2Ω ) = 2.4V.
• Voltage of R ₂ = V ₂ = ( 1.2A )( 3Ω ) = 3.6V.
• Voltage of R ₃ = V ₃ = ( 1.2A )( 5Ω ) = 6.0V.

Check your answers. In a series circuit, the total voltage across all the resistors must be equal to the total voltage of the circuit. ^[3] Add up all the voltages you have calculated and see if we get the full circuit voltage. If that doesn’t work, go back and find the error.

• In our example: 2.4 + 3.6 + 6.0 = 12V, which is the total voltage of the circuit.
• If the sum of the voltages is slightly lower (such as 11.97 instead of 12), you’ve probably rounded the number somewhere. Your answer is still correct.
• Remember that voltage measures the difference in charge, or number of electrons. Imagine you are counting the number of electrons you see as you move along a circuit. If you count correctly, you will eventually get the total charge present in the electrons from start to finish.

Understand what is a parallel circuit. Visualize an electrical cord with one end located at the battery, the other end being split into two separate wires. These two wires run parallel to each other, and then connected again before reaching the other end of the battery. If there is a resistor on the left and right wires, then the two resistors are connected “in parallel”. ^[4]

• Parallel circuits can have an arbitrary number of wires. This instruction still holds true for circuits that are divided into a hundred wires and then reassembled.

Think about how current flows in a circuit. In a parallel circuit, current flows through every line it is supplied with. It will run through the left wire, pass the left resistor, and reach the other end. At the same time, it will also run through the right wire, through the right resistor, and to the other end. No part of the current flows back to or through both resistors in parallel.

Use the full circuit voltage to find the voltage of each resistor. When the voltage of the whole circuit is known, it is surprisingly easy to find the voltage of each resistor. Each parallel wire has the same voltage as the voltage of the whole circuit. ^[5] Suppose a circuit with two resistors in parallel is powered by a 6V battery. The voltage of the left resistor will be 6V and the voltage of the right resistor will also be 6V. It doesn’t matter how big the resistor value is. To understand why, let’s review the series circuit mentioned above:

• Remember that in series circuits, the total voltage of the circuit is always equal to the sum of the voltages of each voltage drop.
• Think of each line path as a series circuit. The same holds true: when you add up the voltages of the whole resistor, you will eventually get the full circuit voltage.
• Since current flows through each wire through only one resistor, the voltage of that resistor must be equal to the total voltage.

Calculate the total current in the circuit. If the problem doesn’t show the full circuit voltage, you’ll have to complete a few more steps. Start by finding the amperage going through that circuit. In a parallel circuit, the total current in the circuit is equal to the sum of the currents passing through each parallel branch. ^[6]

• In mathematical terms: I _sum = I ₁ + I ₂ + I ₃ …
• If it’s confusing, imagine a water pipe split in two. Total water flow is simply the amount of water flowing through each pipe added together.

Calculate the total resistance of the circuit. In parallel circuits, resistors are not as effective because they only hinder the flow of current through a wire or bypass. In fact, the more circuits there are, the easier it is for the current to find its way to the other end. To find the total resistance of the circuit, solve the following equation and find the _total R:

• ¹ / _{R sum} = ¹ / _{R 1} + ¹ / _{R 2} + ¹ / _{R 3} …
• Take for example a circuit with 2 ohm and 4 ohm resistors installed in parallel. ¹ / _{R sum} = 1/2 + 1/4 = 3/4 → 1 = (3/4)R _total → R _sum = 1/(3/4) = 4/3 = ~1.33 ohms.