How To Calculate A Voltage Drop Across Resistors

A simple electrical circuit contains a source of voltage (a power supply, such as a battery, generator or the utility wires coming into your building), a wire to carry current in the form of electrons, and a source of electrical resistance. In reality, such circuits are rarely simple and include a number of branching and re-joining points.

• Voltage (V) is measured in volts (the symbol is also V); current (I) is measured in amperes or "amps" (A); and resistance (R) is measured in ohms (Ω).

Along the branches, and sometimes along the main trunk of the circuit, items such as household appliances (lamps, refrigerators, television sets) are placed, each drawing current to keep itself going. But what exactly happens to the voltage and current within a given electrical circuit set-up from a physics standpoint when each resistor is encountered and the voltage "drops"?

Ohm's law states that current flow is voltage divided by resistance. This can apply to a circuit as a whole, an isolated set of branches or to a single resistor, as you'll see. The most common form of this law is written:

\(V = IR\)

Circuits can be arranged in two basic ways.

Series circuit: Here, current flows entirely along one path, through a single wire. Whatever resistances current encounters along the way simply add up to give the total resistance of the circuit as a whole:

**R_S = R₁ + R₂ + ... + R_N **(series circuit)

Parallel circuit: In this case, a primary wire branches (shown as right angles) into two or more other wires, each with its own resistor. In this case, the total resistance is given by:

**1/R_P = 1/R₁ + 1/R₂ + ... + 1/R_N** (parallel circuit)

If you explore this equation, you find that by adding the resistances of the same magnitude, you decrease the resistance of the circuit as a whole. (Picking 1 ohm, or 1 Ω, makes the math easier.) By Ohm's law, this actually increases the current!

If this seems counterintuitive, imagine the flow of cars on a busy highway served by a single tollbooth that backs up traffic for a mile, and then imagine the same scenario with four more tollbooths identical to the first. This will plainly increase the flow of cars despite technically adding resistance.

If you want to find voltage drops across individual resistors in a series, you proceed as follows:

1. Calculate the total resistance by adding the individual R values.
2. Calculate the current in the circuit, which is the same across each resistor since there is only one wire in the circuit.
3. Calculate the voltage drop across each resistor using Ohm's law.

Example: A 24-V power source and three resistors are connected in series with R₁= 4 Ω, R₂= 2 Ω and R₃ = 6 Ω. What is the voltage drop across each resistor?

First, calculate total resistance: 4 + 2 + 6 = 12 Ω

Next, calculate the current: 24 V/12 Ω = 2 A

Now, use the current to calculate the voltage drop across each resistor. Using V = IR for each, the values of R₁, R₂ and R₃ are 8 V, 4 V and 12 V.

Example: A 24-V power source and three resistors are connected in parallel with R₁= 4 Ω, R₂= 2 Ω and R₃ = 6 Ω, as before. What is the voltage drop across each resistor?

In this case, the story is simpler: Regardless of the resistance value, the voltage drop across each resistor is the same, making the current the variable that differs across resistors in this case. This means that the voltage drop across each is just the total voltage of the circuit divided by the number of resistors in the circuit, or 24 V/3 = 8 V.

See the Resources for an example of an instance in which you can use an automatic tool to calculate the voltage drop in a kind of circuit arrangement called a voltage divider.