Drawing a Circuit When illustrating an electrical circuit for everyone to understand, you must draw a standardized picture called a schematic.When illustrating an electrical circuit for everyone to understand, you must draw a standardized picture called a schematic. A schematic is simply a picture of an electrical circuit that uses standardized symbols to represent the different parts of an electrical circuit.A schematic is simply a picture of an electrical circuit that uses standardized symbols to represent the different parts of an electrical circuit.

Basic Schematic Symbols Battery/ Voltage source Resistor Switch Fuse

Series Circuit Because a series circuit has only one loop, the amount of current that flows through one resistor must be the same amount of current that flows for all the other resistors as well.Because a series circuit has only one loop, the amount of current that flows through one resistor must be the same amount of current that flows for all the other resistors as well..5 A

Series Circuit Because no one resistor is connected directly to both terminals of the power source. No one resistor receives all of the voltage, the voltage is divided out amount each of the resistorsBecause no one resistor is connected directly to both terminals of the power source. No one resistor receives all of the voltage, the voltage is divided out amount each of the resistors 100 V 20 V 50 V 30 V

Kirchhoff’s Voltage Rule We know from the conservation from energy that all the energy that the power source provides must equal the total work that each resistor does.We know from the conservation from energy that all the energy that the power source provides must equal the total work that each resistor does. So then we can say the the energy that each charge has must to be used by all the resistors.So then we can say the the energy that each charge has must to be used by all the resistors. Since voltage is the energy of one charge, we can say that the voltage of the power supply must be used up by all the resistors.Since voltage is the energy of one charge, we can say that the voltage of the power supply must be used up by all the resistors. Kirchhoff’s Voltage lawKirchhoff’s Voltage law –V power supply = Sum of all Voltage drops –V in = V R1 + V R2 + V R3 + V R4 ….

Simplifying a Series Circuit When trying to analyze a series circuit, normally the first step is to reduce the circuit of several resistors to an equivalent circuit of only 1 resistor and 1 power sourceWhen trying to analyze a series circuit, normally the first step is to reduce the circuit of several resistors to an equivalent circuit of only 1 resistor and 1 power source For any simplified circuits we will have a/anFor any simplified circuits we will have a/an –Equivalent Voltage (V eq ) - How much voltage is truly being supplied to the circuit –Equivalent Current (I eq ) - How much current the power source has entering the circuit –Equivalent resistance (R eq ) - How much resistance the circuit actually has –Equivalent power (P eq ) - The total power of the circuit Original Circuit Equivalent Circuit

We can simply a series circuit by using 3 basic principles But we will still need to find the equivalent resistance. V=IR For that we will need to use Ohm’s Law: V=IR Kirrcoff’s Voltage law: V Eq = V R1 + V R2 + V R3 Because there is 1 pathway for current in a series circuit the current for all resistors is the same. I Eq = I R1 = I R2 = I R3 I Eq = I R1 = I R2 = I R3 V in R3R3 R2R2 R1R1 Lets start with a series circuit with 3 resistors

V in R3R3 R2R2 R1R1 Lets start with a series circuit with 3 resistors V eq = V R1 + V R2 + V R3 Because: V eq = V R1 + V R2 + V R3 And since: V = IR I eq R eq = I R1 R 1 + I R2 R 2 + I R3 R 3 We can say: I eq R eq = I R1 R 1 + I R2 R 2 + I R3 R 3 Because All I’s are the same we call each one I IR eq = IR 1 + IR 2 + IR 3 We can say: IR eq = IR 1 + IR 2 + IR 3 The current is a common multiple on both sides Now we have an equation for the equivalent R eq = R 1 + R 2 + R 3 Resistance: R eq = R 1 + R 2 + R 3

Equations for a Series Circuit Equivalent VoltageEquivalent Voltage –V eq = V R1 + V R2 + V R3 …. Equivalent CurrentEquivalent Current –I Eq = I R1 = I R2 = I R3 …. Equivalent ResistanceEquivalent Resistance –R eq = R 1 + R 2 + R 3 … Equivalent powerEquivalent power –Pow Eq = Pow R1 +Pow R2 + Pow R3 …

Sample problem For the circuit shown what is the equivalent resistance? How much current leaves the battery? 300 V 10  For a series R eq = R 1 + R 2 + R 3 R eq = 10  + 10  + 10  R eq = 30  Using Ohms Law: 300 V = I(30  ) I= 10 Amps

Solve a Series Circuit Find the voltage of the battery, the current leaving the battery, and the power of the 5 ohm resistor.    V

Solve a Series Circuit Find the voltage of the battery, the current leaving the battery, and the power of the 5 ohm resistor.    V 3 A

Solve a Series Circuit Find the voltage of the battery, the current leaving the battery, and the power of the 5 ohm resistor.    V 3 A

Solve a Series Circuit Find the voltage of the battery, the current leaving the battery, and the power of the 5 ohm resistor.    V 3 A V 45 V+-

Solve a Series Circuit Find the voltage of the battery, the current leaving the battery, and the power of the 5 ohm resistor.    V 3 A V 45 W 45 V+- V battery = 12V + 45V + 15V = 72 V

Parallel Circuit A parallel circuit is a circuit were each resistor has its own loop, being connected directly to the power source itself. Because of this each resistor receives the full voltage from the power supply.A parallel circuit is a circuit were each resistor has its own loop, being connected directly to the power source itself. Because of this each resistor receives the full voltage from the power supply V -

Parallel Circuit Because each resistor has its own connection to both terminals of the power source each resistor operates independently of all the others, thus each can have their own current, and in one is off the others can still be on.Because each resistor has its own connection to both terminals of the power source each resistor operates independently of all the others, thus each can have their own current, and in one is off the others can still be on. 10 A 6 A 4 A 1 A5 A

Kirchhoff’s Current Rule We know from the conservation of charges that the total charge of a system can not change.We know from the conservation of charges that the total charge of a system can not change. Kirchhoff’s Current rule states when a group of charges enter an intersection of wire, the total number of charges that leave the intersection must equal, the total number of charges that entered the intersection..Kirchhoff’s Current rule states when a group of charges enter an intersection of wire, the total number of charges that leave the intersection must equal, the total number of charges that entered the intersection.. I in I2I2 I1I1 I in = I 1 + I 2

We can simply a parallel circuit by using 3 basic principles But we still need to find the equivalent resistance. For that we will still need to use Ohm’s Law: V=IR Kirchhoff’s Current law: I Eq = I R1 + I R2 + I R3 Because each resistors is connected directly to the power source. V Eq = V R1 = V R2 = V R3 V Eq = V R1 = V R2 = V R3 Lets simplify a parallel circuit with 3 resistors

Finding R eq of a parallel circuit with 3 resistors I eq = I R1 + I R2 + I R3 Because: I eq = I R1 + I R2 + I R3 And since: V = IR or even better I = V/R V eq /R eq ) = V 1 /R 1 ) + V 2 /R 2 ) + V 3 /R e3 ) We have: (V eq /R eq ) = (V 1 /R 1 ) + (V 2 /R 2 ) + (V 3 /R e3 ) Because All V’s are the same we call each one V Now we have an equation for the equivalent (1/R eq )= (1/R 1 ) + (1/R 2 )+ (1/R 3 ) Resistance: (1/R eq )= (1/R 1 ) + (1/R 2 )+ (1/R 3 ) V/R eq ) = V/R eq ) + V/R eq ) + V/R eq ) V/R eq ) We have: (V/R eq ) = (V/R eq ) + (V/R eq ) + (V/R eq ) (V/R eq ) The Voltage is a common multiple on both sides

Equations for a Parallel Circuit Equivalent VoltageEquivalent Voltage –V eq = V R1 = V R2 = V R3 …. Equivalent CurrentEquivalent Current –I Eq + I R1 + I R2 + I R3 …. Equivalent ResistanceEquivalent Resistance –1/R eq = 1/R 1 + 1/R 2 + 1/R 3 … Equivalent powerEquivalent power –Pow Eq = Pow R1 +Pow R2 + Pow R3 …

Two Circuits, but What are They Good for? Series Circuit is great for controlSeries Circuit is great for control –Switches are connect in series to turn things on and off –Fuses are connected in series as to turn the circuit off –“Dimmers”/Rheostats are used in series to regulate the current flow and voltage of another object Parallel is great when you want things to run independentlyParallel is great when you want things to run independently –Power strips –Power outlets of a house –The Different electronics of a car

Sample problem For the circuit shown what is the equivalent resistance? How much current leaves the battery? 300 V 10  For a parallel 1/R eq = 1/R 1 + 1/R 2 + 1/R 3 1/R eq = 1/10  + 1/10  + 1/10  1/R eq = 3/10  Using Ohms Law: 300 V = I(3.33  ) I= Amps R eq = 10/3 

Using the PVIR Box The box is just an easy way to organize the information provided Because V = IR, and P = IV we can use The box to solve any given series or parallel circuit

Solve a Parralell Circuit Find the voltage of the battery, the current leaving the battery, and the power of the 5 ohm resistor. 20  10  5  2 A

Solve a Parralell Circuit Find the voltage of the battery, the current leaving the battery, and the power of the 5 ohm resistor. 20  10  5  2 A - 20 V +

Solve a Parralell Circuit Find the voltage of the battery, the current leaving the battery, and the power of the 5 ohm resistor. 20  10  5  2 A - 20 V + 4 A 1 A

Solve a Parralell Circuit Find the voltage of the battery, the current leaving the battery, and the power of the 5 ohm resistor. 20  10  5  2 A - 20 V + 4 A 1 A 7 A

Solve a Parralell Circuit Find the voltage of the battery, the current leaving the battery, and the power of the 5 ohm resistor. 20  10  5  2 A - 20 V + 4 A 1 A 7 A P = IV P = (4A)(20V) P = 80 Watts