Current FlowConventional Current assumes that current flows out of the positive side of the battery, through the circuit, and back to the negative side of the battery. This was the convention established when electricity was first discovered, but it is incorrect!

Electron Flow is what actually happens. The electrons flow out of the negative side of the battery, through the circuit, and back to the positive side of the battery.

ElectronFlow

Conventional Current

Engineering vs. ScienceThe direction that the current flows does not affect what the current is doing; thus, it doesn’t make any difference which convention is used as long as you are consistent.

Both Conventional Current and Electron Flow are used. In general, the science disciplines use Electron Flow, whereas the engineering disciplines use Conventional Current.Since this is an engineering course, we will use Conventional Current .

ElectronFlow

Conventional Current

Ohm’s Law

Quantities Abbreviations Units SymbolsVoltage V Volts VCurrent I Amperes A

Resistance R Ohms Ω

If you know 2 of the 3 quantities, you can solve for the third.

V=IR I=V/R R=V/I

The mathematical relationship between current, voltage, and resistance

Current in a resistor varies in direct proportion to the voltage applied to it and is inversely proportional to the resistor’s value

Ohm’s Law Chart

VI Rx

Cover the quantity that is unknown.

Solve for V

V=IR

VI R I=V/R

Ohm’s Law ChartCover the quantity that is unknown.

Solve for I

VI R R=V/I

Ohm’s Law ChartCover the quantity that is unknown.

Solve for R

Example: Ohm’s LawThe flashlight shown uses a 6 volt battery and has a bulb with a resistance of 150 . When the flashlight is on, how much current will be drawn from the battery?

VT =+

-VR

IR

Schematic Diagram

mA 40 A 0.04 150V 6

RV I R

R

V

I R

Circuit Configuration

Series Circuits• Components are

connected end-to-end.• There is only a single

path for current to flow.

Parallel Circuits• Both ends of the components

are connected together.• There are multiple paths for

current to flow.

Components (i.e., resistors, batteries, capacitors, etc.)

Components in a circuit can be connected in one of two ways.

Series CircuitsA circuit that contains only one path for current flow

If the path is open anywhere in the circuit, current stops flowing to all components.

Characteristics of a series circuit• The current flowing through every series component is equal.• The total resistance (RT) is equal to the sum of all of the

resistances (i.e., R1 + R2 + R3).

• The sum of all of the voltage drops (VR1 + VR2 + VR3) is equal to the total applied voltage (VT). This is called Kirchhoff’s Voltage Law.

VT

+

-

VR2

+

-

VR1

+ -

VR3

+-RT

IT

Series Circuits

Example: Series CircuitFor the series circuit shown, use the laws of circuit theory to calculate the following:

• The total resistance (RT)

• The current flowing through each component (IT, IR1, IR2, & IR3)

• The voltage across each component (VT, VR1, VR2, & VR3)• Use the results to verify Kirchhoff’s Voltage Law.

VT

+

-

VR2

+

-

VR1+ -

VR3

+-RT

IT

IR1

IR3

IR2

Solution:

V

I R

TR R1 R2 R3 Total Resistance:

TT

T

VI (Ohm's Law)R

Current Through Each Component:

Example: Series Circuit

TR 220 470 1.2 k

TR 1900 1.9 k

T

12 vI 6.3 mAmp1.89 k

T R1 R2 R3

Since this is a series circuit:I I I I 6.3 mAmp

R1 R1V I R1 (Ohm's Law)

Voltage Across Each Component:

V

I R

Example: Series CircuitSolution:

R1V 6.349 mA 220 Ω 1.397 volts

R2 R2V I R2 (Ohm's Law)

R2V 6.349 mA 470 Ω 2.984 volts

R3 R3V I R3 (Ohm's Law)

R3V 6.349 mA 1.2 K Ω 7.619 volts

T R1 R2 R3V V V V

Verify Kirchhoff’s Voltage Law:

Example: Series CircuitSolution:

1.397 2.984 7.619 12 v v v v

12 v 12 v

Parallel CircuitsA circuit that contains more than one path for current flow

If a component is removed, then it is possible for the current to take another path to reach other components.

Characteristics of a Parallel Circuit• The voltage across every parallel component is equal.• The total resistance (RT) is equal to the reciprocal of the sum of the

reciprocal:

• The sum of all of the currents in each branch (IR1 + IR2 + IR3) is equal to the total current (IT). This is called Kirchhoff’s Current Law.321

T

321T

R1

R1

R1

1 R R1

R1

R1

R1

+

-

+

-VR1

+

-VR2 VR3

RT

VT

IT

+

-

Parallel Circuits

For the parallel circuit shown, use the laws of circuit theory to calculate the following:

• The total resistance (RT)

• The voltage across each component (VT, VR1, VR2, & VR3)

• The current flowing through each component (IT, IR1, IR2, & IR3)

• Use the results to verify Kirchhoff’s Current Law.

19

+

-

+

-

VR1

+

-

VR2 VR3

RT

VT

IT

+

-

IR1 IR2 IR3

Example Parallel Circuits

Total Resistance:

volts 15V V V V:circuit parallel a is this Since

R3R2R1T

11 1 1T

1 2 3

R

R R R

Voltage Across Each Component:

Solution:Example Parallel Circuits

11 1 1TR

470 2.2 k 3.3 k

346.59 TR = 350

R1R1

VI (Ohm's Law) R1

V

I R

Current Through Each Component:Solution:

Example Parallel Circuits

R1R1

V 15 vI 31.915 mA=32 mAR1 470

R2R2

V 15 vI 6.818 mA = 6.8 mAR2 2.2 k

.545

R3R3

V 15 vI 4 mA= 4.5mA R3 3.3 k

TT

T

V 15 vI 43.278 mA = 43 mA R 346.59

Verify Kirchhoff’s Current Law:

T R1 R2 R3I I II

Solution:Example Parallel Circuits

43.278 mA=31.915 mA+6.818 mA+4.545 mA

43.278 mA (43 mA) 43.278 mA (43mA)

Kirchoff’s Voltage Law

•The algebraic sum of voltage around a loop is zero.

•Assumption:–Voltage drop across each passive element is in the direction of current flow.

1 2 3 4 0V V V V

+ V2 -

- V4 +

+ V3 1+

V

1

-

-

I

Kirchoff’s Current Law

•Algebraic sum of all currents entering and leaving a node is zero.

•At node A:

•Current entering a node is assigned positive sign. Current leaving a node is assigned a negative sign.

I1

I2

I3A

1 2 3 0I I I

Law of Voltage division

+ VR1 -

R1

+ VR

2 -

R2

-

V

s

+

I

1

1

1 2R s

RV VR R

2

2

1 2R s

RV VR R

Law of Current division

R1 R2

-

V

s

+

I

IR2IR1

2

1

1 2R

RI IR R

1

2

1 2R

RI IR R