Direct Current DC Electric Circuits Series and Parallel

Direct Current (DC) Electric Circuits Series and Parallel AP Physics 1 Montwood High School R. Casao

Electric Current I • An electric current is the movement of positive and/or negative charges Q through a conductor. • Current I is the rate of charge movement through a cross-sectional area of the conductor. The “I” stands for “intensity”.

Electric Current I • The charge carriers in metallic conductors are electrons.

Electric Current I • Charge is measured in coulombs C. • The charge on an electron and a proton is: Q = 1. 602 x 10 -19 C • Current is measured in amperes A;

Two Types of Current • DC current (direct current) is steady a flow of current in one direction.

• AC current (alternating current) direction of current flow changes many times a second. In the US, the frequency of change is 60 Hz. Therefore, the current changes direction 60 times per second.

Electric Circuits • A simple electric circuit will consist of: – A source of energy (in this case a battery). – Conducting wires. – A resistor R that uses the energy. – A switch to open/close circuit. • The source of energy has an internal resistance r.

Conventional vs. Actual Current • Scientists used to believe that positive charges moved through metal wires, but now we know that electrons (negative charges) are what moves. • Conventional current is the hypothetical flow of positive charges that would have the same effect in the circuit as the movement of negative charges that actually does occur. • The direction of conventional current is always from a point of higher potential (positive terminal) toward a point of lower potential (negative terminal).

Schematic Symbols Before 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.

When drawing a circuit, start by drawing the battery first, then follow along the closed loop from the positive terminal of the battery and draw the circuit components until you reach the negative terminal of the battery.

simple circuits Here is a simple electric circuit. It has a battery, a lamp and a switch. wires battery switch lamp The circuit components are connected together with metal connecting wires. When the switch is closed, the lamp lights up because there is a continuous path of metal for the electric current to flow around. If there were any breaks in the circuit, the current could not flow.

Electromotive Force (EMF) • Batteries, generators, and solar cells, transform chemical, mechanical, and radiant energy, respectively, into electric energy. These are examples of sources of EMF. • EMF is measured in Volts V; • The source of EMF provides the energy the charge carriers will conduct through the electric circuit to the resistor.

Potential Difference or Voltage V • Current in a circuit moves from an area of high electric potential energy to an area of low potential energy. This difference in electric potential energy is necessary for current to move through a conductor. • The positive terminal of a battery is the high electric potential energy terminal and the negative terminal is the low electric potential energy terminal. • Potential difference V is also measured in volts.

Chemical Battery Batteries separate positive and negative charges by using a chemical reaction. Chemical potential energy is converted into electrical energy.

Rechargeable Battery Eventually the battery’s chemicals are consumed unless the reaction can be reversed by passing a current into the battery. Automobile battery is recharged while the gasoline engine is running since the engine powers a generator that produces a recharging current. Starting the car Engine running

Potential Difference or Voltage V • Within the battery, a chemical reaction occurs that transfers electrons from one terminal to another. • Because of the positive and negative charges existing on the battery terminals, a potential difference (voltage) exists between them.

Potential Difference or Voltage V • The battery creates an electric field within and parallel to the wire, directed from the positive toward the negative terminal. • This field exerts a force on the free electrons, causing them to move. This movement of charge is known as an electric current. • The current in the circuit is shown to flow from the positive terminal to the negative terminal.

Potential Difference or Voltage V • EMF is the maximum amount of energy per charge the battery can provide to the charge carriers. • Internal resistance r is is the resistance within an electrical device such as a battery or generator. • This resistance causes the actual voltage between the terminals to drop below the maximum value specified by the battery’s EMF. • Voltage or terminal voltage is the energy per charge the charge carriers have after moving through the internal resistance r of the battery. – Some of the energy added to the charge carriers has to be used to travel through the battery. – The remaining energy is carried to the resistors outside the battery. • Mathematically: VT = EMF – (I∙r). • We will often ignore the internal resistance.

Batteries in Series and Parallel:

How can birds perch or squirrels run along high voltage (1000’s of volts) wires and not be cooked? ? To receive a current (shock) there must be a difference in potential between one foot and the other, but every part of the bird or squirrel is at the same potential as the wire. IF they landed with one foot on one wire and the other foot on a neighboring wire at a different voltage, ZAP!!!!!

Resistance R • • Resistance is the opposition to the flow of charge through the conductors. Resistance of a solid conductor depends upon: 1. nature of the material 2. length of the conductor 3. cross-sectional area of the conductor 4. temperature • Resistance is due to the interactions that occur at the atomic scale. • As electrons move through a conductor, they are attracted to the protons in the nucleus of the atoms in the conductor. • The attraction doesn’t stop the electrons, but slows them down a bit and wastes energy.

Resistance • The resistance of a conductor is proportional to the length. – Resistance increases with increased length. • The resistance of a conductor is inversely proportional to the cross-sectional area of the conductor. – Resistance decreases with increased crosssectional area. • Resistance is also dependent upon the temperature of the conductor. Collisions of electrons with other electrons and with atoms raises the temperature of a material as the added heat energy causes the electrons to move faster and hence collide more often. This increases the resistance of the conductor.

Resistance • Resistance is measured in ohms . • Resistivity is related to the nature of the material. Good conductors have low resistivity (or high conductivity). Poor conductors have high resistivity (or low conductivity). • Unit for resistivity is ·m. • Resistance: • Resistivity: = o + o · ·(T – To)

Factors Affecting Resistance

Ohmic and Non-Ohmic Conductors • An ohmic conductor, under constant physical conditions like temperature, has constant resistance for all currents that pass through it. • The slope of the V vs. I graph is a constant for the conductor and provides the resistance R. • A non-ohmic conductor, under constant physical conditions like temperature, has a different resistance for different currents passing through it. • The slope at any point would be the resistance at that particular current value. • Example shown: car headlights.

Ohm’s Law • Ohm's Law deals with the relationship between the voltage and current in a conductor with resistance R. • Ohm’s law applies to ohmic conductors. • Mathematically:

Ohm’s Law “The voltage (potential difference, emf) is directly related to the current, when the resistance is constant” e s e nc ta R= Since , the resistance is the SLOPE of a DV vs. I graph si re = s p lo

Ways to Wire Circuits There 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 another Parallel – between a set of junctions and parallel to each other

Series Circuit • Resistors can be connected in series; that is, the current flows through them one after another. The circuit in Figure 1 shows three resistors connected in series, and the direction of current is indicated by the arrow. Figure 1: Resistors connected in series.

Series Circuit • Since there is only one path for the current to travel, the current through each of the resistors is the same. All the charge carriers that come out of the battery must pass through each resistor. • I = I 1 = I 2 = I 3

Series Circuit • Also, the voltage drops across the resistors must add up to the total voltage supplied by the battery. • The charge carrier will supply energy to each resistor in the circuit; the amount of energy each resistor receives depends upon the resistance itself. • The greater the resistance, the more energy it uses. • E = V 1 + V 2 + V 3

Series Circuit • When working with circuits, it is customary to simplify the circuit by combining resistances in series into a single equivalent resistor Req. • The equivalent resistance Req is the single resistance that could be used in the circuit to replace three separate resistances. • Req or Rtotal = R 1 + R 2 + R 3 • If R 1 = 2 , R 2 = 4 , and R 3 = 8 , the equivalent resistance Req = 2 + 4 + 8 = 14

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.

Series Circuits

Resistors (Light Bulbs) in Series a) When resistors are connected in series, the current through each of them is the same. The sum of the voltage drops across each of them is equal to the voltage of the battery. b) The equivalent resistance Rs of the resistors in series.

Parallel Circuits • Resistors can be connected such that they branch out from a single point and join up again somewhere else in the circuit. This is known as a parallel circuit. • Each of the three resistors is another path for current to travel between points A and B.

Parallel Circuits • Resistors in parallel have the same voltage drop across them. Voltage is constant in parallel. • E = V 1 = V 2 = V 3 • The charge carriers come out of the battery carrying the same joules of energy per coulomb of charge and when they reach the junction point, some charge carriers (i 1) will go through R 1, some will go through R 2 as i 2, and the rest go through R 3 as i 3.

Parallel Circuits • Each charge carrier has the same joules/coulomb no matter which resistor it passes through, which is why the voltage V is constant in parallel. • The sum of the currents in each parallel branch equals the total current entering the parallel branch of resistors. • In this example: i = i 1 + i 2 + i 3 • Usually: IT = I 1 + I 2 + I 3

In 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. Junctions • 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.

DV This junction touches the POSITIVE terminal Notice 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 NEGATIVE terminal

Parallel Circuits • At every junction point in a parallel circuit, the current that enters the junction point must equal the current that exits the junction point. • This is Kirchhoff’s Junction Rule (conservation of charge); Iin = Iout

Parallel Circuits • Resistances in parallel are also simplified into an equivalent resistance Req. • My suggestion involves the reciprocal (x-1) calculator key:

Parallel Circuits • If R 1 = 2 , R 2 = 4 , and R 3 = 8 , the equivalent resistance Req = [(2 )-1 + (4 )-1 + (8 )-1 ] -1 = 1. 14286

Parallel Circuits R 1 = 2Ω R 2 = 4Ω

Advantages of parallel circuits Parallel circuits have two big advantages over series circuits: 1. Each device in the circuit sees the full battery voltage. 2. Each device in the circuit may be turned off independently without stopping the current flowing to other devices in the circuit.

Equivalent Resistance Shortcut • Only works for two resistors in parallel (later for two capacitors in series).

Shortcut Derivation

Resistors (Light Bulbs) in Parallel a) When resistors are connected in parallel, the voltage drop across each of the resistors is the same. The current from the battery divides among the resistors. b) The equivalent resistance of the resistors in parallel is Rp.

Toll Road—Circuit Analogy

Toll Booth Explanation • Adding toll booths in series increases resistance and slows the current flow. • Adding toll booths in parallel lowers resistance and increases the current flow.

• Series connections provide a way to increase total resistance. • Current in the circuit decreases as resistors are added in series. • Parallel connections provide a way to decrease total resistance. • Current in the circuit increases as resistors are added in parallel.

Open Circuit •

Electric Power • Electric power P is the rate of doing electrical work. • Power is the product of current and voltage. • P = V·I • Unit: Watt, W • 1 W = 1 Joule/sec = 1 Volt·Amp • The total power in a series combination of light bulbs and in a parallel combination of light bulbs is the sum of the individual wattages. Ex. : two 60 W light bulbs will dissipate 120 W in a series combination as well as in a parallel combination.

Brightness of a Bulb • The brightness of a bulb depends on the power dissipated by the bulb. • You can remember that from your own experience – when you go to the store to buy a light bulb, you ask for a 60 watt or 75 watt bulb. Watt is the unit of power. • A 75 watt bulb is brighter than a 60 watt bulb when connected to the same voltage, but be careful because a bulb’s power can change depending on the current and voltage it’s hooked up to. • The resistance of a bulb is a property of the bulb itself, and never changes.

Question: A light bulb is rated at 100 W in the United States, where the standard wall outlet voltage is 120 V. If this bulb were plugged in in Europe, where standard wall outlet voltage is 240 V, which of the following would be true? a) The bulb would be ¼ as bright. b) The bulb would be ½ as bright. c) The bulb’s brightness would be the same. d) The bulb would be twice as bright. e) The bulb would be four times as bright. Answer: e The resistance does not change because it is a property of the bulb itself. It will not vary no matter what the bulb is hooked up to. Since P = V 2/R, if the voltage is doubled, the power is quadrupled.

Electric Energy • Electric companies sell you electrical energy. Your energy consumption is computed by expressing power in kilowatts and time in hours. Energy is sold to you in units of k. W-hr. • E = P·t • E = V·I·t

Heating Effects of Current • When a current passes through a conductor, thermal energy is produced (often referred to as Joule heating). • This happens because the mobile charge carriers, such as electrons, make repeated collisions with the atoms of the conductor, causing them to vibrate more and producing an increase in the temperature of the material. • The temperature increase is not related to the direction of the current. • A current in a conductor always generates thermal energy, no matter which direction the current flows. • Devices that use this energy include electric space heaters, stoves, toasters, and fuses.

Fuses & Circuit Breakers Fuse is designed to melt (due to ohmic heating) when current is too large. Circuit breaker does same job without needing replacement; flip the switch to reconnect. Fuse Circuit Breaker

Fuses • A fuse is a ribbon of wire with a low melting point • If the current gets too large, the wire melts or blows out • When fuses blow out, they open the circuit • Once the circuit is open, electricity cannot flow through it

Parts of a Light Bulb • In order to light the bulb, electricity travels through one contact, up the support wires, through the tungsten filament and back down the other support wire to complete the circuit. • What do you think happens in a light bulb when it “burns out”?

Ammeters and Voltmeters • Ammeters are used to measure current and must be placed in series with the circuit component you want to measure the current through. • Voltmeters are used to measure the voltage drop across the resistor or the circuit and must be placed in parallel with the component you want to measure the voltage drop across.