Chapter 3.4-3.8: Current, Resistance and Ohm’s Law

Chapter 3.4-3.8:Current, Resistance and Ohm’s Law

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Current: Going with the flow

• What is current?

– At its simplest, Electric current is the rate of charge flow past a given point in an electric circuit, measured in Coulombs/second – more commonly known as Amperes

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The Ampere (A)

• Current is measured as the number of e- which flow past a particular point per unit time (generally 1 second)

• Saying that a device “draws” 6.24 x 1018 e-/s is unwieldy

• 1A = 1 Coulomb / second– Note: 1 Coulomb = 6.24 x 1018 e-

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50:50 Chance … but they got it wrong!

• Early electronics pioneers assumed that current flowed from (+)ve to (-)ve– This is known as “conventional current”– Comes up multiple times in E.E.

• Turned out to be exactly opposite• We will only consider the correct assertion that

electromotive force is generated by the flow of electrons:– (-)ve battery terminal to (+)ve– Electrons flow anode → cathode

• ACID: anode current into device

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Anodes ..• ACID: Anode current into device– This applies to batteries which are discharging!

• In electronics, the anode is generally the (+)ve terminal of a component such as a diode– Consider how the electrons flow for a moment ..– See how this is maddening?

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Conductors & Insulators

• Conductor:– Any medium which allows the flow of electrical

charge (ie. Electrons)

• Insulator:– Any medium which (ideally) does not allow the

flow of electrical charge– Air breaks down at ~3.3 x 106 V/m or 3.3kV/mm

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Controlling Current

• Two methods to control the current in a circuit:

1. Change the voltage applied to the circuit2. Provide resistance to the flow of electrons

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Controlling Current: Voltage

• By stacking cells of a battery in series, you increase the voltage potential!

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Controlling Current: Resistance

• To influence the flow of electrons (current), you can increase or decrease the ease at which they flow

• Hallway analogy– Long, narrow hallway limits the number of people

which can walk by a point in any given unit of time– Resistors work much the same way

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Resistance: Ohms

• Resistance is defined as the ratio between Voltage (E) and Current (I):

R = E I

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Conductance: mohs ( )℧

• The ability of a material to conduct electricity is measured in Siemens (G)– Conductance is seldom used

• Conductance is effectively the inverse of resistance:– where G = I / E

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Resistors: Common Formats

• There are many resistor packages, depending on design needs

• Resistance value often identified by resistor colour code

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Resistors: Identifying Values15KΩ

276Ω

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Resistors: Identification Example

• The value of the resistor shown above is 339Ω ±1%

93 3 x 10^0 ±1%

Note:10^0 = 1

x 1

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Ohm’s Law

• E = E.M.F. = Voltage (Volts)• I = Current (Amps)• R = Resistance (Ohms)

E = I x R

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Example: Calculate Current

• If a circuit has a 12V battery and a “load” which has a resistance of 10Ω Ohms, what is the current observed in the circuit?

• Recall: E = I * R• I = E / R

• I = 12V / 10Ω• I = 1.2A

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Energy And Work

• Mechanical forms of energy:– Potential– Kinetic

• Electrical energy parallels mechanical– Voltage is often also referred to as potential– Current can be thought of some quantity of

electrons in motion (kinetic)

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Series Resistor Circuit

R1

R2

R3When drawing this schematic, I should have (by convention) labeled theResistors R1 through R3 as the electrons (EMF) flow. I inadvertently labeled them in the direction of conventional current. This is more stylistic than anything else, though it is worth mentioning.

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Series Resistor Circuit

• What do we need to know in order to calculate how much current flows in this circuit?

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Kirchhoff’s Laws

• Loop Rule:– The sum of voltages across all resistors in a series circuit is

equal to the applied EMF– Put another way, the total voltage drop equals the supply

voltage

• Point Rule:– At any node (junction) in a circuit, the sum of currents flowing

into that node is equal to the sum of currents flowing out of that node

– Restated, the current in a loop is the same at every component

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• How much current flows in the following circuit?

• To find the total resistance in a series circuit, simply add the resistances!

Worked Example: Current

E = I / RRearrange the equation to:

I = E / RI = 40V / (5Ω + 25Ω + 10Ω)I = 40V / 40ΩI = 1A

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Worked Example: Voltage Drop

• What is the voltage drop experienced by each component in the following circuit?

• Recall I = 1AE1 = I x R1

E1 = 1A x 5ΩE1 = 5V

E2 = I x R2

E2 = 1A x 25ΩE2 = 25V

E3 = I x R3

E3 = 1A x 10ΩE3 = 10V

+ + = 40V

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Questions?