16.6 Parallel and Series Circuits

Possible Paths

• We are now going to look at the different paths that you can set up for electrons

• Depending on the path you provide, you can control the work that electrons do for you

Tracing electrons

• To better understand circuits, there is one simple way to figure how they will travel – which will determine how the circuit works

• ELECTRONS TAKE THE SHORTEST PATH TOWARDS THE END OF THE CIRCUIT

• ELECTRONS NEVER BACKTRACK

Imagine 2 electrons that are leaving the battery at the same timeWhen they reach the junction they each have a choice: they can move forward or make a turnAt the next junction – the blue electron MUST make a RIGHT turn – this will take it directly towards the POSITIVE POLE of the battery. Likewise, the red electron will continue forward – if it was to turn right, it would move back towards the NEGATIVE POLE of the battery

Series and Parallel Circuits

• There are 2 basic types of circuits • SERIES: there is only one possible

path for the electrons to travel• PARALLEL: there are 2 or more

possible paths for electrons to travel

• This fact gives different properties to series and parallel circuits

Series and Parallel circuits are like roads

SERIES

PARALLEL

Notice:

• Series circuits provide a single path

• Parallel circuits provide multiple paths

• The number of cars that take a path depend on how easy it is to take the path (bigger the road, less traffic)

• Same with electrons – more electrons will take the path with least resistance – so current increases in those paths

Naming loads in circuits

R1

R2

•Resistors are numbered

•Therefore:

•The voltage for R1 is referred to as V1

•The current for R1 is referred to as I1

•RT is the total resistance of the circuit

RT

Sample problem

• Which of the following resistors are parallel to each other, and which are in series?

R1

R2

R3

PARALLEL TO R3

R2 and R3 ARE IN SERIES

Keeping track of V, I, R

• In all circuits, you are always asking yourself what the V, I, and R is of each load in the circuit

• In order to calculate this, you must understand the basic rules associated with each type of circuit

• They were developed by a Russian scientist named Kirchoff and therefore are known as KIRCHOFF’S LAWS (KL)

KL for voltage in Series Circuits

• Because electrons MUST travel through each load in the circuit, they have to give up energy to each one as they do so

• That means the total energy that an electron gives up at each load is equal to what it started with at the start

• VT = V1 + V2 + V3 + …+Vn

Sample question

• In a series circuit, one resistor has a voltage of 3 V and another has a voltage of 2 V. What is the total voltage provided by the battery?

V1

V2

VT

KL for current in a series circuit

• Since a series circuit provides no other pathway – the current stays constant at all points

• It is like a single water pipe that has no back up – the flow of water is the same at the start as it is in the middle and the end – since water from the back pushes water at the front

• IT = I1 = I2 = I3 = … = I4

Sample problem

• The current leaving a battery that is connected to a series circuit is measured as being 5 A. What is the current moving through the two resistors in the circuit?

I1

I2

IT

KL for voltage in parallel circuits

• In a parallel circuit, electrons only have to move through the loads that are in their paths

• That means that each electron only has to give up energy to the load in their path

• Each electron gives up the same amount of energy

• So the voltage of resistors parallel to each other are equal to each other

• VT = V1 = V2 = V3 = … = Vn

I1

I2

IT

Sample problem

• Two parallel resistors are attached to a battery providing 9 V of power. What is the voltage across the two resistors?

VT

V1

V2

KL law for current in parallel circuits

• In parallel circuits, electrons split up

• That means the current splits up

• If you add up the current in each path, you will have the total current of the circuit

• IT = I1 + I2 + I3 + … + In

IT

Sample problem

• A parallel circuit has 2 resistors. If the total current leaving the battery is 10 A, and the first resistor has a current of 2 A, what is the current in the second resistor?

IT

I1

I2

Kirchoff’s Laws for Resistance

• Using Ohm’s Law and KL for voltage and current in parallel and series circuits, the resistance of each type of circuit can also be analyzed as well

KL for Resistance in Series Circuits• In a Series circuit, since:

• VT = V1 + V2 + V3 + …+Vn

• And V = IR• Then:• IRT = IR1 + IR2 + IR3 + …+IRn

• Therefore: since the I values are the same, they cancel out on both sides giving:

• RT = R1 + R2 + R3 + …+Rn

KL for Resistance in Parallel Circuits• In a parallel circuit, since:• IT = I1 + I2 + I3 + … + In• And I = V/R, therefore:• V/RT = V/R1 + V/R2 + V/R3 + .. +

V/Rn

• Since the voltage value is the same in a parallel circuit, the V’s cancel out on the RS and LS giving:

• 1/RT = 1/R1 + 1/R2 + 1/R3 + .. + 1/Rn