41099 Chap.2 Kirchhoff's laws, dividers and electrical power
Kirchhoff's laws, dividers and electrical power
What this chapter covers
- 01
A node, and why charge cannot accumulate at one
- 02
Declaring a sign convention before writing a node equation
- 03
What counts as a loop, and the node rule that disqualifies most wrong ones
- 04
Series and parallel combination derived from the two laws rather than memorised
- 05
The voltage divider rule and the ratio that sets a node voltage
- 06
The current divider rule, and why the other branch appears in the numerator
Set a node voltage with a series pair, then check the current it costs
- 3Identify which of the two resistors the wanted voltage sits across.
- 3Apply the divider ratio with that resistance in the numerator.
- 2Evaluate, then confirm the remaining voltage and the chain current.
Key terms
- Node
- A connection of two or more elements in a circuit.
- Loop
- A path that leaves a node, passes through elements and returns without visiting any node twice.
- Current law
- The rule that the currents at any node sum algebraically to zero.
- Voltage law
- The rule that the voltages around any loop sum algebraically to zero.
- Equivalent resistance
- The single resistance that would draw the same current as a combination under the same voltage.
- Voltage divider
- A series resistor pair that splits a supply voltage in proportion to the two resistances.
- Current divider
- A parallel resistor pair that splits an entering current in inverse proportion to the two resistances.
Kirchhoff's laws, dividers and electrical power FAQ
How do you know which resistance belongs on top of a divider ratio?
The numerator is always the resistance the wanted voltage appears across. For a junction voltage measured to ground that is the lower resistor, and for the drop across the upper resistor it is the upper one. Writing that sentence before substituting numbers removes the entire family of inverted ratio errors, and it is the step a marker looks for.
Why is the numerator inverted in the current divider rule?
Both branches of a parallel pair see the same voltage, so the branch with less resistance carries more current. The other branch's resistance therefore has to sit on top. If the rule slips, set one resistance to zero mentally and ask where all the current would obviously go; the expression that agrees with that answer is the correct one.
Does a path that crosses the same junction twice count as a loop?
No. The definition requires that you return to the starting node without visiting any node more than once. A path that doubles back through a junction it has already used is not a loop, and writing a voltage sum for it produces a relation that is simply untrue. Trace the path with a finger and count junction visits before writing anything down.
Two dividers give the same fraction with very different resistances. Which should be built?
It depends entirely on what will draw current from the junction. A low resistance pair holds its voltage better under load but wastes standing current continuously. A high resistance pair wastes almost nothing but sags as soon as anything pulls on it. Neither is correct in general, and being able to name the trade off is the answer being assessed.
Should the combination rules be memorised or derived?
Derive them once from the two laws and the memory takes care of itself. Series follows from the voltage law with a shared current, parallel follows from the current law with a shared voltage. A question that alters the arrangement slightly is answerable from the laws and usually not from a memorised expression.
Assessment move
Start every circuit question by writing one sentence naming what is shared, a current or a voltage. That single line chooses the combination rule, the divider rule and the power form for you. Sanity check each result against a bound: a junction voltage lies between zero and the supply, and a parallel combination resists less than its smallest branch.
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