Electric Current and Resistance

Physics

Potential DifferenceCharges can “lose” potential energy by

moving from a location at high potential (voltage) to a location at low potential.

Charges will continue to move as long as the potential difference (voltage) is maintained.

Potential Difference =Voltage=EMF

In a battery, a series of chemical reactions occur in which electrons are transferred from one terminal to another. There is a potential difference (voltage) between these poles.

The maximum potential difference a power source can have is called the electromotive force or (EMF), . The term isn't actually a force, simply the amount of energy per charge (J/C or V)

CurrentA sustained flow of electric charge past

a point is called an electric current.Specifically, electric current is the rate

that electric charge passes a point, so

Current = or I = q/tCharge

time

Measuring Current If 1 Coulomb of charge (6.25 x 1018

electrons) passes a point each second, the current is 1 Ampere.

So, 1 Ampere = 1 Coulomb/sec

Ampere (for Andre’ Ampere)

Usually called an ampOpen Circuit – break in the circuit, no current flow

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Voltage SourceA battery or electrical outlet is a source

of electric potential or voltage - not charge.

The electrons that move in a conductor are supplied by the conductor - not the voltage source.

The net charge on a current-carrying conductor is zero.

Electromotive ForceAn old-fashioned term for electric

potential or voltage is “electromotive force” or “emf”.

Electrical ResistanceMost materials offer some resistance to

the flow of electric charges through them. This is called electrical resistance.

ResistanceResistance (R) – is defined as the restriction of electron

flow. It is due to interactions that occur at the atomic scale. For example, as electron move through a conductor they are attracted to the protons on the nucleus of the conductor itself. This attraction doesn’t stop the electrons, just slows them down a bit and causes the system to waste energy.

The unit for resistance is the OHM,

ResistanceResistance of a conductor depends on:

Material - Gold is best Length - longer conductors have more

resistance. Cross section - thick wires have less

resistance than thin wires Temperature - higher temperature means

more resistance for most conductors

Ohm’s LawFor many conductors, current depends

on:Voltage - more voltage, more current

Current is proportional to voltageResistance - more resistance, less

current Current is inversely proportional to

resistance

Ohms’ Law In symbols:

V = IRVI R

George Simon Ohm (1787-1854)

The actual values depend on the resistance of the conductor

Called Ohm’s LawR – resistance measured in Ohms ()

I V

IR V

Ohm’s Law“The voltage (potential difference, emf) is directly

related to the current, when the resistance is constant”

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Voltage vs. Current

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Current(Amps)

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Since R=V/I, the resistance is the SLOPE of a V vs. I graph

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Direct Current If the voltage is maintained between

two points in a circuit, charge will flow in one direction - from high to low potential. This is called direct current (DC)

Battery-powered circuits are dc circuits.

Alternating Current If the high & low voltage terminals

switch locations periodically, the current will flow “back and forth” in the circuit. This is called alternating current (AC).

Circuits powered by electrical outlets are AC circuits.

AC in the US In the US, current changes direction

120 times per second, for a frequency of 60 cycles per second or 60 Hertz.

Normal outlet voltage in the US is 110-120 volts, although some large household appliances run on 220-240 volts.

Converting AC to DCAC is converted to DC using devices

called diodes, which allow charges to move in only 1 direction.

Speed of Electrons

Electrons in a circuit do not move quickly - they actually “drift” at about 1 mm/s.

It is the electric field that moves quickly - at about the speed of light - through the circuit and carries the energy.

Electrical POWERWe have already learned that POWER is the rate at which work

(energy) is done. Circuits that are a prime example of this as batteries only last for a certain amount of time AND we get charged an energy bill each month based on the amount of energy we used over the course of a month…aka POWER.

POWERIt is interesting to see how certain electrical

variables can be used to get POWER. Let’s take Voltage and Current for example.

Other useful power formulas

These formulas can also be used! They are simply derivations of the POWER formula with different versions of Ohm's law substituted in.

Ways to Wire CircuitsThere are 2 basic ways to wire a circuit. Keep in

mind that a resistor could be ANYTHING ( bulb, toaster, ceramic material…etc)

Series – One after anotherParallel – between a set of junctions and parallel to each other

Schematic SymbolsBefore you begin to understand circuits you need to be able to

draw what they look like using a set of standard symbols understood anywhere in the world For the battery

symbol, the LONG line is considered to be the POSITIVE terminal and the SHORT line , NEGATIVE.The VOLTMETER and

AMMETER are special devices you place IN or AROUND the circuit to measure the VOLTAGE and CURRENT.

Closing the switch establishes a potential difference (voltage) and an electric field in the circuit.

Electrons flow in a net direction away from the (-) terminal.

High Potential

Low Potential

Conventional CurrentBy tradition,

direction in which “positive charges” would flow.

Direction is opposite of electron flow.

The Voltmeter and AmmeterThe voltmeter and ammeter cannot be just placed anywhere in the circuit. They must be used according to their DEFINITION.

Since a voltmeter measures voltage or POTENTIAL DIFFERENCE it must be placed ACROSS the device you want to measure. That way you can measure the CHANGE on either side of the device.

Voltmeter is drawn ACROSS the resistorSince the ammeter measures the current or FLOW it must be placed in such a way as the charges go THROUGH the device.

Current goes THROUGH the ammeter

Voltmeter

Measures the voltage between two points in an electric circuit.

Must be connected in parallel.

AmmeterMeasures electric current.

Must be placed in series.

Simple CircuitWhen you are drawing a

circuit it may be a wise thing to start by drawing the battery first, then follow along the loop (closed) starting with positive and drawing what you see.

Series CircuitIn in series circuit, the resistors

are wired one after another. Since they are all part of the SAME LOOP they each experience the SAME AMOUNT of current. In figure, however, you see that they all exist BETWEEN the terminals of the battery, meaning they SHARE the potential (voltage).

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As the current goes through the circuit, the charges must USE ENERGY to get through the resistor. So each individual resistor will get its own individual potential voltage). We call this VOLTAGE DROP.

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;Note: They may use the terms “effective” or “equivalent” to mean TOTAL!

ExampleA series circuit is shown to the left. a) What is the total resistance?

b) What is the total current?

c) What is the current across EACH resistor?  

d) What is the voltage drop across each resistor?( Apply Ohm's law to each resistor separately)

R(series) = 1 + 2 + 3 = 6

V=IR 12=I(6) I = 2A

They EACH get 2 amps!

V12 V V3=(2)(3)= 6V V2=(2)(2)= 4V

Notice that the individual VOLTAGE DROPS add up to the TOTAL!!

Parallel CircuitIn a parallel circuit, we have

multiple loops. So the current splits up among the loops with the individual loop currents adding to the total current

It is important to understand that parallel circuits will all have some position where the current splits and comes back together. We call these JUNCTIONS.

The current going IN to a junction will always equal the current going OUT of a junction.

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Parallel CircuitNotice that the JUNCTIONS both touch the POSTIVE and NEGATIVE terminals of the battery. That means you have the SAME potential difference down EACH individual branch of the parallel circuit. This means that the individual voltages drops are equal.

This junction touches the POSITIVE terminal

This junction touches the NEGATIVE terminal

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To the left is an example of a parallel circuit. a) What is the total resistance?  

b) What is the total current?  

c) What is the voltage across EACH resistor?   d) What is the current drop across each resistor? (Apply Ohm's law to each resistor separately)

2.20

3.64 A

8 V each!

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1.6 A 1.14 A 0.90 A

Notice that the individual currents ADD to the total.

Compound (Complex) CircuitsMany times you will have series and parallel in the SAME circuit.

Solve this type of circuit from the inside out.

WHAT IS THE TOTAL RESISTANCE?

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Suppose the potential difference (voltage) is equal to 120V. What is the total current?

1.06 A

What is the VOLTAGE DROP across the 80 resistor?

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What is the VOLTAGE DROP across the 100 and 50 resistor?

35.2 V Each!

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What is the current across the 100 and 50 resistor?

0.352 A

0.704 A

Add to 1.06A

The End