CIE A Level Physics: Understanding Kirchhoff's Laws in Circuit Analysis

Kirchhoff's First Law

The sum of the currents entering a junction always equal the sum of the currents out of the junction.

Junction

A point where at least three circuit paths meet.

Branch

A path connecting two junctions.

Current in a Series Circuit

The current is the same at all points in a series circuit.

Current in a Parallel Circuit

The current divides at each junction in a parallel circuit.

Kirchhoff's Second Law

The sum of the e.m.f's in a closed circuit equals the sum of the potential differences.

Conservation of Charge

Current shouldn't decrease or increase in a circuit when it splits.

Conservation of Energy

The energy transferred into the circuit is equal to the energy transferred out of the circuit.

Potential Difference in Series Circuit

The sum of the potential difference across each component is equal to the total e.m.f of the power supply.

Potential Difference in Parallel Circuit

The potential difference is the same across each closed loop.

Combined Resistance in Series

The combined resistance of two or more resistors is the sum of the individual resistances.

Equation for Combined Resistance in Series

R = R1 + R2 + ...

Independent Series Circuit

Each circuit loop acts as a separate, independent series circuit.

Resistors in Series

When two or more components are connected in series, the combined resistance of the components is equal to the sum of the individual resistances.

Potential Difference in Resistors in Series

Resistors connected in series each have their own separate potential difference.

Examiner Tip for Junctions

Drawing arrows on the diagram for the current flow at each junction will help with understanding.

Closed Circuit Loop

A closed circuit loop acts as its own independent series circuit and each one separates at a junction.

Parallel Circuit Utility

A parallel circuit is made up of two or more closed loops, allowing current to flow through the rest of the lights and appliances if one light breaks.

Current Conservation at Junction

The current I into the junction is equal to the sum of the currents out of the junction.

Energy Transfer in Circuit

The total potential difference across the components is the sum of the potential difference across each individual component.

Circuit Complexity

As circuits become more complex, it can be confusing as to which currents are into the junction and which are out.

Worked Example Resistance

The combined resistance R in the following series circuit is 60 Ω.

Combined Resistance (Series)

Sum of individual resistances: R = R1 + R2 + ...

Potential Difference in Series

Each resistor has a separate voltage drop.

Example Resistance Calculation

Given R = 60 Ω, R2 = 20 Ω.

Resistors in Parallel

Components connected across the same voltage.

Combined Resistance (Parallel)

Reciprocal of total resistance: 1/R = 1/R1 + 1/R2 + ...

Current in Parallel

Current splits at junctions among resistors.

Voltage in Parallel

Same voltage across all parallel resistors.

Reciprocal of a Number

1 divided by the number.

Example Parallel Calculation

Combined resistance of equal resistors halves.

Kirchhoff's Laws

Principles for analyzing current and voltage in circuits.

Ammeter

Measures current in a circuit.

Voltmeter

Measures potential difference across components.

Example Current Calculation

A1 = 0.270 A from series connection.

Example Voltage Calculation

V1 = 10 V from Kirchhoff's second law.

Resistance Calculation Step

Rearranging R2 = R - (R1 + R3).

Combined Resistance Decrease

Total resistance in parallel is less than individual.

Current Division

Current splits inversely to resistance values.

Total Resistance Formula

RT = 1 / (1/R1 + 1/R2 + ...).

Common Mistake

Leaving answer as 1/R without calculating R.

Energy Sharing in Parallel

Equal energy distribution among resistors.

Voltage Drop Calculation

V3 = 24 V - 2 V for potential difference.

Example Resistance Value

Combined resistance of 3 resistors equals 2R.