Electrical Circuits

~Moving Charge Put to Use

The Circuit• All circuits, no matter how simple or complex, have one

thing in common, they form a complete loop.• As mentioned before, circuits should have various circuit

elements in the loop.• These vary depending on the design of the circuit.

Circuit Symbols• Each circuit element has its own symbol. • Common circuit symbols are shown below.

Resistor

Switch

Wire Battery

Voltmeter

Ammeter

A Conductor of Current

Opens and Closes Circuits

Provides Resistance to Current Flow

Source of DC Charge Flow

Measures Current

Measures Voltage

More Circuit Symbols• Here are some additional circuit symbols that you may see.

Potentiometer

AC Source

Ground

Crossing

Junction

Capacitor DiodeStores Charge on Plates

Variable Resistor

Provides AC Current

Drains Excess Charge Buildup

Only Allows Current to Flow One Way

All Four Wires Connect

Wires Only Cross and do not Connect.

Circuit Diagrams• Circuit diagrams employ the use of the circuit symbols as

opposed to drawing an actual picture for each circuit.• This simplifies and standardizes circuit pictures.• Compare the picture below to the circuit diagram below.

Circuit Picture Circuit Diagram (Schematic)

The Series Circuit• Look at the circuit below. Two resistors are connected in

a series configuration.• Notice there is only one path for current to flow. There

are no branches in the circuit, which would allow charge to take multiple paths.

• Since there is only one path, the current everywhere in the circuit is constant, even through the resistors.

R1

R2

A break at any point in the circuit will result in the stoppage of current flow.

1 2eqI I I

The Series Circuit (cont.)• Every series configuration can be reduced to a single

value for resistance known as the equivalent resistance, or Req.

• The formula for Req is as follows for series:

• This can be used as a step to solve for the current in the circuit or the voltage across each resistor.

R1

R2

Req

1 2eqR R R

Sample Problem (Series)• A circuit is configured in series as shown below.

– What is the equivalent resistance (Req)?

– What is the current through the circuit?(Hint: Use Ohm’s Law.) 10

20

30

6V

1 2 3eqR R R R 10 20 30eqR 60eqR

eq eqeq eq

eq eq

V VR I

I R

660eq

VI

0.1eqI A

Ieq = 0.1A

606V

Sample Problem (Series) (cont.)• We still have one question to ask. What are the voltages

across each resistor?

– For the 10 Resistor:

– For the 20 Resistor:

– For the 30 Resistor:

• What do you notice about thevoltage sum?

10

20

30

6V

Ieq = 0.1A

VR V IRI

V IR 0.1 10V A

0.1 20V A

0.1 30V A

1V V

2V V

3V VV IR

V IR

Voltages across resistors in series add to make up the total voltage.

1 2 3 6V V V V 6 eqV V

Series Circuit Summary• There are several facts that you must always keep in

mind when solving series problems.– Current is constant throughout the entire circuit.

– Resistances add to give Req.

– Voltages across each resistor add to give Veq.

– Make use of Ohm’s Law.

1 2eqI I I

1 2eqR R R

1 2eqV V V

V VR V IR II R

Devices that Make Use of the Series Configuration

• Although not practical in every application, the series connection is crucial as a part of most electrical apparatuses.– Switches

• Necessary to open and close entire circuits.– Dials/Dimmers

• A type of switch containing a variable resistor (potentiometer).

– Breakers/Fuses• Special switches designed to shut off if current is too

high, thus preventing fires.– Ammeters

• Since current is constant in series, these current-measuring devices must be connected in that configuration as well.

The Parallel Circuit• Look at the circuit below. The resistors have been

placed in a parallel configuration.• Notice that the circuit branches out to each resistor,

allowing multiple paths for current to flow.• One way to test if two resistors are in parallel is to see if

there are exactly two clear paths from the ends of one resistor to the ends of the other resistor.

R1 R2

Branch

X

BranchX

A break in one of the branches of a parallel circuit will not disable current flow in the remainder of the circuit.

The Parallel Circuit (cont.)• Notice how every resistor has a direct connection to the

DC source. This allows the voltages to be equal across all resistors connected this way.

• An equivalent resistance (Req) can also be found for parallel configurations. It is as follows:

R1 R2

1 2eqV V V

Req

1 2

1 1 1

eqR R R

The Parallel Circuit (cont.)• Do you like rivers?• Parallel circuits are kind of like rivers with branches in them. • Is the current in each branch equal to the total current of the river?• No, the total current is equal to the sum of the current in each

branch.• Thus, the individual currents add to form the total current.

1 2eqI I I

IeqIeqI1

I2

Sample Problem (Parallel)• A circuit is configured in parallel as shown below.

– What is the equivalent resistance of the circuit?

30 6V

1 2 3

1 1 1 1

eqR R R R

1 1 1 130 30 60eqR

11 1 130 30 60

eqR

12eqR

126V

Sample Problem (Parallel)• What is the current in the entire circuit?

• What is the current across each resistor?

30 6V

eq eqeq eq

eq eq

V VR I

I R 6

12eqVI

0.5eqI A

VIR

630VI

660VI

0.2I A 0.1I A

The 30 Resistors The 60 Resistor

Parallel Circuit Summary• There are several facts that you must always keep in

mind when solving parallel problems.– Voltage is constant throughout the entire parallel circuit.

– The Inverses of the Resistances add to give the inverse of Req.

– Current through each resistor adds to give Ieq.

– Make use of Ohm’s Law.V VR I V IRI R

1 2eqV V V

1 2eqI I I

1 2

1 1 1

eqR R R

Devices that Make Use of the Parallel Configuration

• Although not practical or safe in every application, the parallel circuit finds definite use in some electrical apparatuses.– Electrical Outlets

• Constant voltage is a must for appliances.– Light Strands

• Prevents all bulbs from going out when a single one burns out.

– Voltmeters• Since voltage is constant in parallel, these

meters must be connected in this way.

Combination Circuits• Some circuits, such as the one shown below, have

series/parallel combinations in their configurations.• Many of these can be reduced using equivalent

resistance formulas, while some cannot.• Do you see the combinations within this circuit?• Now let’s solve a problem involving this circuit.

R2R1

R3 R4

SeriesParallel

Sample Problem (Combo)• A combination circuit is shown below.• What is the equivalent resistance (Req) of the circuit?

– First, we must identify the various combinations present.

Series

Parallel

1 2eqR R R 10 30eqR

40eqR 1 2

1 1 1

eqR R R

1 1 120 20eqR

10eqR

Series Parallel

1040

301020 20

25V

Sample Problem (Combo)• The simplified circuit only shows the equivalent

resistances. Is the circuit now fully simplified?• No, we must identify the final configuration. What is it?• It’s a series configuration.

Series

Parallel

1040

301020 20

25V

4010

25V1 2eqR R R 40 10eqR 50eqR

Series

50

Sample Problem (Combo)• The circuit is further simplified below. Can it be

simplified again?• No, the circuit is completely simplified.• What is the current in the entire circuit?

4010

25V

Series

50

5025V

eq eqeq eq

eq eq

V VR I

I R 25

50eqVI

0.5eqI A

Conclusion• In order to approach any circuit problem, you must know

the circuit symbols well.• All the circuits that you will be given will be series,

parallel, or a combination of both that is solvable.• Ultimately, keeping a working knowledge of the

properties of each circuit type is key. You may want to make a note card that contains all of these facts.