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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.
Note 
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