Kirchhoff's Laws (KCL & KVL)
A three-node DC network uses an ideal voltage source between N₁ and N₀, a series pair R₁–R₂ through junction N₂, and a toggleable third resistor R₃ in parallel with the same nodes as the source. Node voltage V(N₂) follows the voltage-divider formula; KCL at N₂ gives I₁ = I₂; with R₃ present, KCL at N₁ adds I₃ = V/R₃ to the source current.
Who it's for: Introductory circuits and lab prep before mesh/nodal analysis; pairs with the Wheatstone bridge and Ohm’s law pages.
Key terms
- Kirchhoff current law
- Kirchhoff voltage law
- node voltage
- voltage divider
- parallel branch
How it works
A fixed three-node DC network: an ideal voltage source sets the top node, a series pair **R₁–R₂** forms a junction **N₂**, and an optional third resistor **R₃** connects the same nodes as the battery (parallel load). **Kirchhoff’s current law** at **N₂** makes the series branch a single current; **KVL** around the **R₁–R₂** loop recovers the voltage-divider result. Adding **R₃** does not change **V(N₂)** in this ideal model, but it increases the total current drawn from the source.
Key equations
Frequently asked questions
- Why does R₃ not change V(N₂)?
- The ideal voltage source fixes N₁ relative to N₀, so the series branch R₁–R₂ still sees the same terminal voltage V; the divider result for V(N₂) is unchanged. R₃ only changes how much extra current the source must supply.
- Is putting R₃ parallel to an ideal battery realistic?
- Physically a real battery has internal resistance; here the ideal model isolates the algebra of KCL/KVL. Treat R₃ as a load in parallel with the rest of the circuit for bookkeeping practice.
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