Solving a series circuit comes down to three steps: add up all the resistances, use Ohm’s Law to find the current, then calculate the voltage drop across each component. Once you understand the rules that govern series circuits, every problem follows the same pattern.
Three Rules That Define a Series Circuit
A series circuit has one single path for current to flow. Components are connected end to end, like beads on a string. Before you touch any math, you need to internalize three rules that make series circuits predictable:
- Current is the same everywhere. Because there’s only one path, every component carries the identical current. If 2 amps flows through the first resistor, 2 amps flows through the second and third as well. Written out: I_total = I_1 = I_2 = I_3.
- Resistances add up. The total resistance of the circuit equals the sum of every individual resistance: R_total = R_1 + R_2 + R_3 + … This is true for any number of resistors.
- Voltage drops add up to the source voltage. The battery’s voltage gets divided among the components. A larger resistor claims a larger share. The individual voltage drops must sum to exactly the supply voltage. This principle is known as Kirchhoff’s Voltage Law.
These three rules are all you need. Every series circuit problem is some combination of applying them.
Step-by-Step Method
Step 1: Find Total Resistance
Add every resistance value in the circuit together. If you have resistors of 100 Ω, 200 Ω, 300 Ω, and 400 Ω, the total resistance is simply 100 + 200 + 300 + 400 = 1,000 Ω. This single number represents the entire circuit’s opposition to current flow.
Step 2: Find Total Current
Apply Ohm’s Law using the source voltage and the total resistance you just calculated. Ohm’s Law states that current equals voltage divided by resistance: I = V / R. If the battery supplies 20 V and total resistance is 1,000 Ω, the current through the entire circuit is 20 / 1,000 = 0.02 A, or 20 milliamps. Remember, this same current flows through every component.
Step 3: Find Each Voltage Drop
Now use Ohm’s Law on each resistor individually. Multiply the current (which you just found) by each resistor’s value:
- 100 Ω resistor: 0.02 A × 100 Ω = 2 V
- 200 Ω resistor: 0.02 A × 200 Ω = 4 V
- 300 Ω resistor: 0.02 A × 300 Ω = 6 V
- 400 Ω resistor: 0.02 A × 400 Ω = 8 V
Step 4: Check Your Work
Add up all the individual voltage drops: 2 + 4 + 6 + 8 = 20 V. That matches the source voltage exactly, confirming the calculations are correct. If your voltage drops don’t sum to the battery voltage, something went wrong in an earlier step.
Calculating Power
Many problems also ask how much power each component uses. Power measures how quickly electrical energy converts to heat (or light, or motion). You can calculate it three ways, all equivalent:
- P = I × V (current times voltage)
- P = I² × R (current squared times resistance)
- P = V² / R (voltage squared divided by resistance)
Using the example above, the power dissipated by the 300 Ω resistor would be 0.02² × 300 = 0.12 watts. The total power consumed by the circuit equals the sum of each resistor’s individual power, or you can compute it directly: P_total = I × V_source = 0.02 × 20 = 0.4 watts. The individual powers (0.04 + 0.08 + 0.12 + 0.16) add to 0.4 W, which checks out.
Reading a Circuit Diagram
On a schematic, resistors appear as either a zigzag line (common in the U.S.) or a small rectangle (international standard). The lines extending from either end are the terminals that connect to the rest of the circuit. In a series diagram, you’ll see each resistor connected one after another in a single loop, with a battery symbol completing the path. If every component sits along one unbroken loop with no branching junctions, you’re looking at a series circuit.
What Happens When Something Breaks
Series circuits have one critical weakness: if any single component fails or a wire breaks, the entire circuit stops working. Because there’s only one path for current, a break anywhere interrupts current everywhere. This is called an “open fault.” Think of old-style Christmas lights where one burned-out bulb killed the whole string.
This same property is used intentionally in safety designs. Many lawnmowers wire two switches in series so that both must be pressed before the motor runs. If either switch is released, the circuit opens and the blade stops.
Common Mistakes to Avoid
The most frequent error is confusing series rules with parallel rules. In a series circuit, you add resistances directly. In a parallel circuit, you use the reciprocal formula, which is entirely different. If a problem gives you a circuit and you’re not sure which type it is, look for branching paths. No branches means series.
Another common slip is using the source voltage when calculating current through a single resistor. Each resistor only “sees” its own voltage drop, not the full battery voltage. When you apply Ohm’s Law to an individual component, use that component’s voltage and resistance. The source voltage only pairs with the total resistance.
Finally, watch your units. Resistances in kilohms (kΩ) need to be converted to ohms before plugging into formulas, or your current will be off by a factor of 1,000. Similarly, if current comes out in milliamps, make sure you use 0.02 A rather than 20 mA when multiplying, unless you’re comfortable adjusting the result afterward.
Solving When You’re Missing a Value
Not every problem hands you all the resistances and the voltage. Sometimes you know the total current and need to work backward. The approach stays the same, just rearranged. If you know the current and the source voltage, Ohm’s Law gives you total resistance (R = V / I). If you know total resistance and are missing one resistor’s value, subtract the known resistances from the total. If you know a voltage drop across a specific resistor and the current, you can find that resistor’s value (R = V / I).
The key insight is that Ohm’s Law (V = I × R) works at every level of the circuit. It applies to the whole circuit using total values, and it applies to each individual component using that component’s values. You always have three variables per component. If you know any two, you can find the third.