Download SPH 3U Electricity and Magnetism Lesson 3: Kirchhoff`s Voltage and

SPH 3U Electricity and Magnetism Lesson 3: Kirchhoff’s Voltage and Current Laws
Voltage and Current behave very differently in series circuits and parallel circuits (and in series and parallel
branches of large, complicated circuits). Kirchoff’s Laws allow us to analyze how they will behave (and then
build large, complicated circuits to do things for us).
Kirchhoff’s Voltage Law: In any complete path (full loop from start to finish) in an electric circuit, the total
electric potential increase at the source (or sources) is equal to the total electric potential decrease
throughout the rest of the circuit.
This is kind of like conservation of energy again.
This means that in the sum of voltage gains and drops in a complete path in a circuit must be zero.
So in a series circuit, with only one complete path,
Vseries = V1 + V2 + V3 + …
ex)
then Vseries, the voltage across the source in a series circuit, is equal to
the voltage across each of the loads in the source added together.
The 10 volts by the battery is a potential rise.
The 8 volts by the resistor is a potential drop.
The other resistor must have a voltage of 2 volts,
to make the potential rises and drops equal.
But in a parallel circuit, with many possible paths for the electricity,
Vparallel = V1 = V2 = V3 = …
ex)
Demonstration:
then Vparallel, the voltage across the source in a parallel circuit, is equal to the
voltage across each of the loads throughout the parallel circuit.
Always seemed like a bit of a magic trick… maybe Kirchhoff’s Current Law can help explain how this works.
Kirchhoff’s Current Law: In a closed circuit, the amount of current entering a junction is equal to the amount
of current exiting a junction. Again, this is like conservation of energy- electrons aren’t created or destroyed as
they move through a current (their potential energy changes instead).
So in a series circuit, with only one complete path,
Iseries = I1 = I2 = I3 = …
then Iseries, the current through the source, is equal to the current at any point
in the circuit.
ex)
But in a parallel circuit, with many possible paths for the electricity,
Iparallel = I1 + I2 + I3 + …
then Iseries, the current through the source, is equal to sum of the current going
through each parallel branch of the circuit
ex)
Applying Kirchhoff’s Laws to a Mixed Circuit:
Find all unknowns
Vsource = 40 V
Lamp 1 = 10 V
Lamp 3 = 20 V
Isource = 0.4 A
Lamp 3 = 0.1 A