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 time When they reach the junction they each have a choice: they can move forward or make a turn At 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 R1R1 R2R2 Resistors are numbered Therefore: The voltage for R 1 is referred to as V 1 The current for R 1 is referred to as I 1 R T is the total resistance of the circuit RTRT

Sample problem Which of the following resistors are parallel to each other, and which are in series? R1R1 R2R2 R3R3 PARALLEL TO R 3 R 2 and R 3 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 V T = V 1 + V 2 + V 3 + …+V n

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? V1V1 V2V2 VTVT

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 I T = I 1 = I 2 = I 3 = … = I 4

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? I1I1 I2I2 ITIT

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 V T = V 1 = V 2 = V 3 = … = V n I1I1 I2I2 ITIT

Sample problem Two parallel resistors are attached to a battery providing 9 V of power. What is the voltage across the two resistors? VTVT V1V1 V2V2

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 I T = I 1 + I 2 + I 3 + … + I n ITIT

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? ITIT I1I1 I2I2

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: V T = V 1 + V 2 + V 3 + …+V n And V = IR Then: IR T = IR 1 + IR 2 + IR 3 + …+IR n Therefore: since the I values are the same, they cancel out on both sides giving: R T = R 1 + R 2 + R 3 + …+R n

KL for Resistance in Parallel Circuits In a parallel circuit, since: I T = I 1 + I 2 + I 3 + … + I n And I = V/R, therefore: V/R T = V/R 1 + V/R 2 + V/R V/R n Since the voltage value is the same in a parallel circuit, the V’s cancel out on the RS and LS giving: 1/R T = 1/R 1 + 1/R 2 + 1/R /R n