Kirchhoff’s Circuit Laws, explained.
Kirchhoff’s laws express current conservation at a circuit node and voltage balance around a closed loop under lumped-circuit assumptions.
Why it happens
Two resistor-divider midpoints are linked by ten ohms. Solving their two nodal equations yields midpoint voltages, bridge current and equal source and return currents; a lower-right resistance of thirty balances the bridge.
Kirchhoff’s laws express current conservation at a circuit node and voltage balance around a closed loop under lumped-circuit assumptions.
Read the result
At balance the midpoint potentials match, so connecting the bridge does not create midpoint current. Source and return currents still need not be zero.
A worked example
Find the null in a resistor bridge
Keep the fixed divider resistors at ten, twenty and fifteen ohms.
Adjust the lower-right resistor to thirty ohms and inspect equal midpoint potentials.
Open and reconnect the bridge, confirming zero cross-current at balance while the source still supplies the divider branches.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Two resistor-divider midpoints are linked by ten ohms. Solving their two nodal equations yields midpoint voltages, bridge current and equal source and return currents; a lower-right resistance of thirty balances the bridge.
Where this idea is useful
A practical use
Use a null measurement to compare resistance ratios without assuming every branch carries the same current.
A common misconception
“A zero bridge current means the entire circuit has no current.”
Equal midpoint potentials remove that branch’s driving voltage, while other complete branches can still carry current.
What this explanation leaves out
- The circuit is ideal and steady. Transients, inductive fields, source resistance, thermal changes and measurement loading beyond the stated bridge resistor are absent.
Why solve nodal equations instead of adding all resistors?
The connected bridge is not a simple series chain; node balance accounts for how currents split and recombine.
Which node or loop conservation statement constrains the quantity you want to infer?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.