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Kirchhoff's Circuit Laws

Four DC circuits — a single loop, three resistors in series, three in parallel, and a two-loop network driven by two cells — solved live by Kirchhoff's laws. Charge carriers drift along each wire at a speed set by that branch's current, resistors glow with the power they dissipate, and the readout walks each loop term by term so you can watch the voltages add up to exactly zero.

Key formulas

$V = IR$
Ohm's law
$V$
Voltage across the resistorV
$I$
CurrentA
$R$
ResistanceΩ
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$\sum_{\text{into node}} I = \sum_{\text{out of node}} I$
Junction rule (KCL)
$I$
Branch current at the nodeA
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$\sum_{\text{closed loop}} \Delta V = 0$
Loop rule (KVL)
$\Delta V$
Potential change across each elementV
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$I = \dfrac{V_{\text{from}} - V_{\text{to}} + E}{R}$
Current in a branch of EMF E and resistance R
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$V_{\text{term}} = E - I r$
Terminal voltage of a real cell
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$P = I^{2} R$
Power dissipated in a resistor
$P$
PowerW
$I$
CurrentA
$R$
ResistanceΩ
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What you can change

Circuit layout
EMF of each cell
Internal resistance of each cell
The three resistances

Key concepts

Kirchhoff's current law (junction rule) as charge conservation
Kirchhoff's voltage law (loop rule) as energy conservation
Ohm's law and equivalent resistance in series and parallel
EMF, internal resistance and terminal voltage
Power delivered by a cell and dissipated as heat
Sign conventions: a negative branch current means a cell is charging

Read the full theory: Kirchhoff's Circuit Laws Explained →

Kirchhoff's Circuit Laws

Key formulas

Ohm's law

Junction rule (KCL)

Loop rule (KVL)

Current in a branch of EMF E and resistance R

Terminal voltage of a real cell

Power dissipated in a resistor

What you can change

Key concepts

Kirchhoff's Circuit Laws Explained

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