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.

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

I₁ = I₂ (no storage at N₂)

V = I₁R₁ + I₂R₂

I₂ = V(N₂)/R₂ , V(N₂) = V · R₂/(R₁+R₂)

KCL at N₁: I_total = I₁ + I₃ , I₃ = V/R₃

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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Frequently asked questions

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