In a straight wire, the current is constant, but the voltage is divided.
In a steady-state series circuit, the same current passes through every resistor. Since Vᵢ = IRᵢ, a larger resistance has a larger voltage drop. The sum of the voltage drops across the resistors equals the source voltage.
If the source voltage is V, then V = I(R₁ + R₂), the total resistance is R₁ + R₂. Adding a series resistor will decrease the overall current from the same voltage source. The current does not decrease as it is consumed by the front resistor and decreases as it moves towards the back.
In parallel circuits, the voltage is equal, and the current divides.
The resistors connected to the same two points receive the same voltage. The current in each branch is Iᵢ = V/Rᵢ, and the total current entering at the junction is the sum of the branch currents. Smaller resistors experience a larger current flow.
Therefore, 1/R the combined resistance = 1/R₁ + 1/R₂. The combined resistance of the two resistors can also be calculated as R₁R₂/(R₁ + R₂), and it is smaller than the smallest branch resistance. When the same DC voltage source is added to the branch, the total current increases, but the voltage of the existing branch remains constant.
Comparing only the connection arrangement
We are comparing series and parallel connections using two identical resistors and a constant power supply voltage. It is necessary to determine whether the ammeter is measuring the entire path or a specific branch in order to correctly interpret the measurement values. Even with the same symbol “I,” the meaning can differ depending on where the ammeter is located.
Actual circuits can exhibit a decrease in terminal voltage when the overall current increases due to internal resistance. This is one reason why a parallel circuit, modeled with an ideal voltage source, and a real light bulb circuit can appear differently. The underlying formula used here disregards the effects of connection wires and instruments.
Key relationships and symbols
R_series = R₁ + R₂ · 1/R_parallel = 1/R₁ + 1/R₂ · I_total = ΣI_branch
| Symbol | Meaning | Unit |
|---|---|---|
| R_equivalent | Total resistance seen by the source | Ω |
| I_total | Current supplied by the source | A |
| I_branch | Current in each parallel branch | A |
| V | Voltage between two nodes | V |
Worked example
If you connect 10 Ω and 20 Ω with 6 V, what happens?
In a series circuit, the total resistance is 30 Ω, the current is 0.2 A, and the voltage is divided into 2 V and 4 V. In a parallel circuit, each branch has a current of 0.6 A and 0.3 A, and the total current is 0.9 A; the total resistance is approximately 6.67 Ω.
Common misconceptions
- In a series circuit, the current is constant for each resistor, but the voltage is not necessarily the same.
- The equivalent resistance when resistors are connected in parallel is not simply the sum of the individual resistances.