Lesson summary
10.2.1 Kirchhoff’s First Law — AS PHYSICS 9702 notes: State Kirchhoff’s first law and apply it to series and parallel circuits.Statement — the sum of the currents entering a junction is always equal to the sum of the currents leaving the same junction.Basis — a consequence of con…
- Current division
- Each junction
- Series ammeters
- Resistance
- Components
- Reciprocal
Section 1 of 8Kirchhoff’s first law
1Statement
- Statement the sum of the currents entering a junction is always equal to the sum of the currents leaving the same junction.
2Basis
- Basis a consequence of conservation of charge.
3Meaning
- Meaning current should not decrease or increase when a circuit splits.
Section 2 of 8Junctions and branches
Junction
- Junction a point where at least three circuit paths meet.
Branch
- Branch a path connecting two junctions.
Splitting
- Splitting the current before a split equals the sum of the currents after it.
Section 3 of 8Series circuits
- Current
- it is the same at any point in a series circuit.
Section 4 of 8Parallel circuits
Current division
- Current division the current divides at the junctions and each branch can have a different value.
Each junction
- Kirchhoff’s first law applies at each junction.
Section 5 of 8Applying the law
Applying the law
Draw arrows for the current at each junction, from positive to negative.
Write total current in = total current out.
Rearrange for the unknown, for example 270 mA = A3 + 80 mA gives A3 = 190 mA.
- Series ammeters
- an ammeter in series with a known current reads that same current.
Section 6 of 8More from the specification
1
Current conservation and power balance
- Current conservation and power balance verifying junction current equality confirms charge conservation while establishing accurate branch parameters for computing electric power.
2
Kirchhoff's first law and charge conservation
- The algebraic sum of all electric currents entering any circuit junction equals the sum of currents leaving the junction, expressing conservation of electric charge.
- (Sigma Iin = Sigma Iout)
3
Combined resistance of parallel resistors
- Applying Kirchhoff's first law shows that the reciprocal of equivalent resistance equals the sum of reciprocals of parallel branch resistances: 1/Rtotal = 1/R1 + 1/R2.What the symbols mean: RT = total resistance of resistors in parallel (Ω), always smaller than the smallest one · R1, R2 = the separate resistances (Ω)
4
Branch current calculation
- In parallel networks with equal applied voltage, current through each branch is inversely proportional to branch resistance according to Ohm's law: I = V / R.
5
Parallel resistor formula equation
- Parallel resistor formula equation combined resistance of parallel components equals the reciprocal of the sum of reciprocal values of individual resistors.
6
Potential difference across parallel branches
- Potential difference across parallel branches parallel circuit components share identical potential difference across their terminals,
- allowing current branch calculations.
7
Circuit problem solving methods
- Circuit problem solving methods applying conservation of charge at junctions simplifies complex network problems containing multiple interconnected resistors and branches.
8
Voltmeter
- Instrument that measures p.d., connected in parallel.
9
Potential difference
- Work done by a unit charge passing through a component.
10
Combined resistance
- Single resistance that could replace several resistors.
11
Closed circuit
- Complete loop with a source in which current can flow
12
Energy transferred
- W = V Q, in joules.What the symbols mean: E or W = energy transferred (J) · Q = charge (C) · V = potential difference (V) · I = current (A) · t = time (s)
13
Resistance
- Opposition to current, R = V / I, in ohms (Ω).
14
Components
- Perpendicular parts of a vector that add to give the vector.
15
Reciprocal
- The value 1/x; the calculator button is x−1.
16
R
R1 + R2 + ...
What the symbols mean: RT = total resistance of resistors in series (Ω) · R1, R2 = the separate resistances (Ω)
17
R
R1 + R2 + ... = R1 + R2 + R3
What the symbols mean: RT = total resistance of resistors in series (Ω) · R1, R2 = the separate resistances (Ω)
Section 7 of 8Key terms
| Term | Meaning |
|---|---|
| Kirchhoff’s first law | Sum of currents into a junction equals sum of currents out. |
| Junction | Point where at least three circuit paths meet. |
| Branch | Path connecting two junctions. |
| Conservation of charge | Charge is neither created nor destroyed. |
Section 8 of 8Exam technique
1
Mixing up currents entering and leaving a junction — draw arrows first.
2
Applying the law at points with only two paths where it is trivial.
3
Forgetting to convert mA to A.
4
Thinking current is used up in a component — it is the same around a series loop.