Meaning and mechanism
The law of currents states that there is a conservation principle based on the fact that charge does not continuously accumulate at the contact points. It involves adding the incoming current and the outgoing current, with attention to their signs.
The law of potential difference states that the change in potential along a path returning to the same point is canceled out. It distinguishes between the rise in potential when passing through a power source and the drop in potential due to resistance.
Relationships and conditions
Set ΣI=0 at a node and ΣV=0 around a closed loop, then solve together with Ohm’s law. A negative result relative to the chosen current direction means that the actual current flows the other way.
The model assumes lumped circuit elements. If changing magnetic flux links a loop, include the induced EMF rather than summing electrostatic potential differences alone.
What to observe in the simulation
The algebraic sum of currents at a junction and voltages around a closed loop is zero.
This is a fixed circuit with two ideal DC sources and three resistors. Wire resistance and meter loading are omitted. Use buttons to select the probe position. Use this simulation; do not reproduce it with real power supplies or wall outlets.
Key relationships and symbols
I₁ + I₂ − I₃ = 0 · E₁ − I₁R₁ − I₃R₃ = 0
| Symbol | Meaning | Unit |
|---|---|---|
| ΣI | Signed sum of currents at a node | A |
| ΣV | Signed sum of voltage changes around a closed loop | V |
Worked example
If I₁=5 mA and I₂=−4 mA, what is I₃ leaving the junction?
1 mA
Common misconceptions
- It is not necessarily incorrect to say that the calculated current is negative – it could simply be in the opposite direction of the reference direction.