Intermediate · 12 min
Series and parallel circuits
Find equivalent resistance and use current and voltage rules in simple resistor networks.
One path in series
Series components share one path, so the same current passes through each. Their voltage drops add to the supply voltage. For resistors in series, total resistance is the sum: Rtotal = R₁ + R₂. Use this total with Ohm's law to find circuit current, then find each voltage drop using its own resistance. These models assume ideal wires and a supply whose stated voltage is maintained.
Worked example
A 2 Ω resistor and a 4 Ω resistor are in series across 12 V. Total resistance = 6 Ω; current = 12 ÷ 6 = 2 A Voltage drops = 4 V and 8 V
Branches in parallel
Parallel branches connect across the same two points, so they have the same voltage. The total current is the sum of branch currents. Equivalent resistance obeys 1/Rtotal = 1/R₁ + 1/R₂. For two positive resistances, the equivalent is smaller than either one because there is an additional conducting path. Equal parallel resistors have equivalent resistance equal to one resistance divided by their number.
Worked example
Two 8 Ω resistors are connected in parallel. Equivalent resistance = 8 ÷ 2 = 4 Ω
Compare circuit drawings
- On paper, connect two 6 Ω resistors in series across 12 V. Calculate the total current.
- Draw them in parallel across the same ideal supply. Calculate each branch current and the total current.