Series & parallel circuits
The hard part isn't the formula — it's keeping track of current and voltage when resistors combine. So build the circuit and watch. Change the battery or a resistor and every reading updates by Ohm's law, V = IR. The current even flows faster where it's larger.
The rules you're seeing
Ohm's law
V = I × R. Voltage across a resistor equals the current through it times its resistance. Everything on this page comes from this one line.
Series
Same current through every resistor. Resistances add up (R = R₁+R₂+R₃), and the voltages across them add to the battery voltage.
Parallel
Same voltage across every branch. The total resistance is less than the smallest resistor (1/R = 1/R₁+1/R₂+1/R₃), and branch currents add up.
Power
P = V × I. More current or more voltage means more power — which is why parallel bulbs draw more from the same battery than series ones.
Part of the Electricity chapter — read the notes, grab the formula sheet and take the quiz. One of Priodemy for School, free with every EduSuite school.
Series and parallel, and why the difference matters
The one rule underneath everything
Every reading in this simulator comes from Ohm's law, V = IR, applied repeatedly. There is no separate theory for series and parallel circuits; there are only two facts about how components share current and voltage, and Ohm's law does the rest.
In a series circuit there is a single path, so the same current flows through every component. The voltages divide, adding up to the battery voltage, and resistances simply add: R = R₁ + R₂ + R₃. Adding another resistor always increases the total resistance and therefore reduces the current everywhere.
In a parallel circuit every branch is connected across the same two points, so each branch has the full battery voltage across it. The current divides instead, and the reciprocals add: 1/R = 1/R₁ + 1/R₂. The consequence surprises people — adding a resistor in parallel decreases the total resistance, because you have opened another path for current. The combined resistance is always smaller than the smallest individual branch.
Why your house is wired in parallel
This is the practical payoff of the topic, and it follows directly from the two rules above. If household appliances were in series, switching off one would break the single path and everything else would go dead, and each appliance would receive only a fraction of the supply voltage. Wired in parallel, every appliance gets the full 220 V, and each can be switched independently without affecting the others. The cost is that total current rises as you add appliances, which is exactly what a fuse or MCB is there to limit.
What to try
- Build a series circuit and make one resistor much larger than the others. Watch it take most of the voltage — a potential divider, seen directly.
- Switch to parallel and add branches one at a time. Total resistance falls, total current climbs, but each existing branch keeps its own current unchanged.
- Compare power dissipation using P = I²R in series and P = V²/R in parallel, and note which resistor runs hottest in each case. In series it is the largest resistor; in parallel it is the smallest.
Mistakes that cost marks
Forgetting to invert at the end. The parallel formula gives you 1/R, not R. Stopping one step early is the most common arithmetic slip in this chapter, and the giveaway is an answer larger than the individual resistances — impossible for a parallel combination.
Assuming current is "used up". Current is not consumed by a resistor. Whatever flows into a component flows out of it; what changes is the energy each charge carries, which appears as the potential drop. In a series circuit the ammeter reads the same wherever you place it.
Applying series logic to a parallel branch. When a circuit mixes both, reduce it in stages: collapse each parallel group to a single equivalent resistance first, then treat the result as a series chain. Trying to handle the whole network in one step is where most errors enter.