RECALL?? Electricity concepts in Grade 9. Sources of electrical energy Current Voltage Resistance Power Circuits : Series and Parallel

Unit 3C Circuits

RECALL?? Electricity concepts in Grade 9. Sources of electrical energy Current Voltage Resistance Power Circuits : Series and Parallel

2 Types of Electricity Electrostatics Electricity that is not in motion. Current Electricity Electricity that is in motion. Occurs whenever an electric charge moves through a conductor.

2 Types of Current Electricity Direct Current (DC) Electricity that ONLY flows in one direction. Typical in circuits operating with cells (batteries) Alternating Current (AC) Electricity that moves back and forth at regular intervals. Typically found in household circuits. In North America we have 110 V operating at 60 Hz In Europe they have 220 V operating at 50 Hz.

Definition of Electric Current Electric Current is the amount of electrons (or charge) that flows through a cross sectional area of a conductor per a certain period of time. Amount of charge Current time # of electrons X elemental charge time I e - Q t ne t UNITS?? Q t Amperes C A I s

Example: Find the amount of current in a wire that has 10.0 C of charge passing through every 2.0 seconds.

Direction of Direct Current Consider a simple circuit Conventional Flow: Electricity was thought to have traveled from the abundance of electricity (positive) to the deficiency of electricity (negative) This was thanks to Ben Franklin

Unfortunately Ben got it wrong. It is actually electrons that flow in a circuit. Electron Flow: Electrons travel away from the negative of a cell, through the circuit, and are attracted towards the positive of the cell. However many university still use conventional flow when talking about the direction electricity flows

Electric Potential (VOLTAGE) Recall??: and Now we have Q I so Q It t E VQ V( It) Units?? V e Ee E e Q VIt Ee VQ

Examples: 1. What is the energy used by a 10.0 Amp lawn mower that operates for 1 hour using 110 Volts?

2. How long would it take a A) computer monitor operating at 120 V and drawing 0.8 A of current to consume 3.96 MJ of energy? B) heater operating on 240 V drawing 20 A of current?

3. One electron volt (1 ev) is a unit of energy we use when dealing with elemental particles in Nuclear Physics. 1 ev is the energy given to an electron as it is accelerated through a potential difference of 1 volt. What is the energy equivalent of 1 ev measured in Joules? 1eV Ee VQ 1V 1.60 10 19 C 1 ev 1.60 10 19 J

Circuits

Consider the diagram below. This is a picture of a circuit.

A schematic uses symbols to represent the components of a circuit. It makes circuits much easier to draw and read. Symbols used for schematics are basically universal with slight variations from text to text.

Wires crossed But NOT connected Wires crossed AND connected

Jump Back Draw the circuit above using these schematic symbols.

What are the energy transformations that occur when the switch is closed? In the source the electrons are given potential energy (in a cell this would be due to chemical action). (Voltage RISE) As the electrons "fall" through the circuit, they give up most of their energy In the resistor the electrons release their energy in the form of heat. (Voltage DROP)

In the light bulb the energy is given up in the form of: Heat Light Sound (sometimes you can hear a filament vibrating.) (Voltage DROP) An insignificant amount of energy is lost due to heating in the connecting wires. Also some energy will be lost in the source itself. It is part of the circuit and it does have an internal resistance. We do NOT usually include these last 2 in any circuit calculations in 3204.

NOTE: The light bulb and resistor are called LOADS. The cells are called SOURCES. This is a series circuit because there is only one path that electrons can take. In a parallel circuit electrons have a choice of directions that they can travel The ammeter measures current. It is connected in series with the light bulb. The electrons (current) that travel through the light bulb must travel through the ammeter.

Law of Conservation of Electric Charge Electric charge cannot be created or destroyed in an electric circuit, nor does it accumulate at any point in the circuit. Therefore, the amount of charge approaching a particular point in a circuit must equal the amount of charge leaving that point. The charge can't "pile up". Based on this what could we say about the current in a series circuit? The current in a series circuit is the same everywhere.

Law of Conservation of Electric Energy As electrons move through an electric circuit they gain energy in the sources and lose energy in the loads, but the total energy gained in one trip is equal to the total energy lost. Therefore a reasonable hypothesis would be "the total voltage rises in a circuit will equal the total voltage drops."

How do we determine these drops and rises? with a voltmeter. voltmeters are connected in parallel with whatever you are measuring. How could we measure the voltage drop across the load (light bulb)? place a voltmeter in "parallel" with the light bulb. Draw the voltmeter on the schematic.

Circuit Analysis

Kirchhoff's voltage rule: "Around any complete path through an electric circuit, the sum of the increases in electric potential is equal to the sum of the decreases in electric potential."

Examples: 1. Vo V1 V V 2 3 240V 80V V 100V 2 240V 80V 100V V2 V2 60V 60V What type of circuit is this? Series

2. What type of circuit is this? Parallel. There is a choice of paths electrons can take Both are 12 V because each parallel branch represents a complete path through the circuit.

3. V 1 = 5 V V 0 = V 2 = 3 V V 3 = What type of circuit is this? Hybrid. It has a combination of series with a parallel branch. Both sections of the parallel branch have the same voltage.

4. V 1 = 2 V V 0 = 5 V V 2 = V 3 = V 4 = V 8 = V 7 = 1 V V 6 = 1 V

Circuit Rules for Current Draw a schematic diagram of an electrical source and an ammeter connected at a node or junction to two parallel branches, each of which contains a light bulb and an ammeter.

A A A 1 2 3 What do the arrows on the schematic represent? Electron Flow If A 2 = 1.5 A and A 3 = 2.5 A, what do you think A 1 would read? 4 A

From the Law of the Conservation of Electric Charge, we can say that the current entering a junction in an electric circuit will equal the current leaving the junction. Kirchhoff's current rule: At any junction point in an electric circuit the total electric current into the junction is equal to the total electric current out. I 0 = I 1 + I 2 + I 3 +...

For example: I = o I = I + I + I 0 1 2 3 I = 2.5A I = 4.0A I = 6.0A 1 2 3

Example I 1 = I 0 = 5 A I 2 = I 3 =

Circuit Guidelines: In each part of a series circuit, the loads have the same current. In each part of a parallel circuit, each load has only part of the current. In series circuits, each load uses only part of the total potential energy (voltage). In parallel circuits, each load has the same voltage.

Solve the following: 1. Find x

2.

3. V 1 = 2 V I 1 = V 0 = V 2 = I 2 = 2 A I 3 = 1 A V 3 = V 4 = 2 V I 4 = 0.2 A I 0 =

RESISTANCE IN ELECTRIC CIRCUITS Resistors Resistors are conductors, but electrons lose some of their energy as they pass through the resistor. Thus resistors are considered to be voltage drops. Some uses for resistors are: (i) to produce light (tungsten in lamps) (ii) to produce heat (electric stoves, heaters) (iii) to control voltage and current (electronic circuits) This is to prevent certain circuit components from frying!

RESISTANCE IN ELECTRIC CIRCUITS Consider a simple circuit where a resistor is connected to a battery. Draw this circuit. How do we measure the current in the circuit? Place an ammeter in series. How do we measure the voltage drop in the resistor? Place a voltmeter in parallel with the resistor. Resistors

Lets vary the voltage and see what happens to the current. APPLET I V V Set resistance to 2 W Voltage Max 10 V Current Max 3 A 0 1 2 3 4 5 6 I

What is the slope of this line?? 2 V A What was the resistance of the resistor? 2 W What is the relationship between the resistance and the slope of the Voltage vs Current graph? They are EQUAL For a certain resistor, R, the voltage drop across R is directly proportional to the current passing through R.

Thus, V I To equate this relation the proportionality constant is the resistance of the resistor, R. OR V I V R I V RI which also represents the slope of the voltage vs current graph. This relationship is called OHM s Law

RESISTANCE IN ELECTRIC CIRCUITS Resistors A resistor is called a linear circuit element because it is fairly independent of the current passing through it. In such cases a graph of V versus I gives a straight line with slope, R. A resistor is ohmic because it obeys Ohm's Law, where the ratio of constant. V I is

NOTE: There are non-ohmic devices which are not linear. They do not follow Ohm's Law. EX: a diode light emitting diode LED

An I - V graph for a 30 (ma) Silicon Diode 20 Reverse 10 Forward -12.0 Bias Bias Knee Voltage Break Down Voltage -11.8-0.6-0.4-0.2 V (volts) 0.2.4.6.8 This is definitely NOT Linear!!

OHM'S LAW The potential difference between any two points in a conductor varies directly to the current between the two points. V R I W V A R- resistance measured in ohms (W - omega) V- voltage or potential difference measured in volts (V) I - current measured in amperes (A)

Problems: 1. 2. 6V V= 6V V= I=0.25A I= R= R= 80 W

OHM S Law Worksheet The Boys Kirchhoff and Ohm Worksheet

Physics 3204 The Boys - Kirchhoff and Ohm 1. Most people can feel a current of about 1 ma. Currents of a few ma cause pain but rarely much damage in a healthy person. Currents of 10 ma cause severe contraction of the muscles, and a person may not be able to release the source of the current.. Death from paralysis of the respiratory system can occur. If the current is above 70 ma and passes across the torso the heart may begin to contract irregularly and blood is not properly pumped. Strangely enough, if the current is much larger, on the order of 1A, the damage may be less and death by heart failure may be less likely under some conditions. The amount of current that will pass through our bodies depends on the bodies resistance. Living tissue has quite low resistance since the fluid of cells contains ions that can conduct quite well. However the outer layers of skin, when dry, offer much resistance. The effective resistance between two points on opposite sides of the body when the skin is dry is approximately 10 5 W. When the skin is wet the resistance may be 10 3 W( or less.)

A) What amount of current would a person suffer with dry skin that came in contact with 120 V? What would be the result of this current? B) What amount of current would a person suffer with wet skin that came in contact with 120 V? What would be the result of this current? C) What amount of voltage would a person with dry skin have to come in contact with to receive a shock of (i)1 ma (ii) 3 ma (iii) 10 ma (iv) 70 ma (v) 1 A

Finding Total Resistance in Series V 0 R 0 I 0 Consider V 1 R 1 I 1 V 3 R 3 I 3 V 2 R 2 I 2 What can we say about the currents? ALL Equal I 1 = I 2 = I 3 = I 4 What about the voltages? Voltage Rise = Voltage Drop V V V V 0 1 2 3

To derive an equation for resistance in series, we start with the voltage equation: V V V V 0 1 2 3 Divide each term by I 0 V0 V1 V2 V3 I I I I 0 0 0 0 Since ALL currents are equal in series we can rewrite the above equation as: V0 V1 V2 V3 I I I I 0 1 2 3

Recall Ohm s Law So, V0 V1 V2 V3 I I I I 0 1 2 3 V R I R R R R T 1 2 3 and R becomes The total resistance, R T, of n resistors connected in series is : T V I 0 0 R R R R R T... 1 2 3 n

R 2 = 5W Example 1. Find the total resistance R 1 = 3W R 3 = 10W

2.What is the voltage drop across R 1 in the circuit below?

NOTE: If there are n resistors ALL of the same resistance, say R, connected in series then R R R R R T... 1 2 3 n R R R R... R T R added n times RT nr 2. Find the total resistance of five 20 W resistors connected in series RT nr 5 20W

Finding Total Resistance in Parallel V 0 R 0 I 0 Consider V 1 R 1 I 1 V 2 R 2 I 2 V 3 R 3 I 3 What can we say about the Voltages? ALL Equal V 1 = V 2 = V 3 = V 4 What about the Currents? I I I I 0 1 2 3

To derive an equation for resistance in parallel, we need to get resistance into the current equation: I I I I 0 1 2 3 V so V R I I R Rewrite the currents in V0 V1 V2 V3 RT R1 R2 R3 Since ALL voltages are equal in parallel we can rewrite the above equation as: V0 V0 V0 V0 R R R R T 1 2 3 I I I I 0 1 2 3

Divide each term by V 0 V0 V0 V0 V0 V R V R V R V R 0 T 0 1 0 2 0 3 Cancel the V 0 1 1 1 1 R R R R T 1 2 3 The total resistance, R T, of n resistors connected in parallel is : 1 1 1 1 1... R R R R R T 1 2 3 n

Example 1. Find the total resistance R 1 = 3W R 2 = 2W R 3 = 6W

Example 2. Find the total resistance R 1 = 8W R 2 = 12W

3. What current, I, is coming from the source in the circuit below? Which resistor has the: (i) Greatest resistance (ii) Least resistance

Note: The total resistance of resistors connected in parallel is always less than the smallest resistance The total resistance of resistors connected in series is always greater than the largest resistance

If there are n resistors ALL of the same resistance, say R, connected in parallel then 1 1 1 1 1... RT R1 R2 R3 Rn 1 1 1 1 1... R R R R R T 1/R added n times R 1 R T T n R R n

Example: Find the total resistance of twenty(20) 5 W resistors connected in Parallel Series If this was connected to 120V find A) total current If this was connected to 120V find A) total current B) current through each resistor B) current through each resistor

Circuit Analysis In more interesting circuits there are combinations of parallel and series branches. (Hybrid Circuits) Each branch can be replaced by a single equivalent resistance.

1. Find the current drawn from the 12 V battery if each resistance is 2 W R 1

2. What is the total resistance of the circuit below?

Physics 3204 Worksheet 1. Find the total resistance when the following resistors are connected in series: A). W, 9.8 W B) 0 W, 0 W, 0 W C).0 W, 0 W, 0 W 2. Find the total resistance when the following resistors are connected in parallel: A).0 W,.0 W B) 00 W, 00 W C) 00 W, 00 W, 00 W D) 0 W, 00 W, 00 W,

4. For the circuits below find the missing values: A) 2.0W

B)

5. For each circuit below, find the current through and the potential drop across each resistor. A)

B)

Worksheet 2

V(V) I(A) R(W) R 1 R 2 R 3 R T

V(V) I(A) R(W) R 1 R 2 R T

V(V) I(A) R(W) R 1 R 2 R 3 R T

V(V) I(A) R(W) R 1 R 2 R 3 R 4 R T

V(V) I(A) R(W) R 1 R 2 R 3 R 4 R 5 R 6 R T

V(V) I(A) R(W) R 1 R 2 R 3 R 4 R T

Power in Electric Circuits Joules Law Power Rules in Circuits Cost of Electricity

RECALL 2204 E Work Power Formula P t time This is know as Joule s Law UNITS?? E J P t s = W (watts)

What is E in circuit Problems? E = VIt E VIt P t t P VI P is the power dissipated by a current I through a potential difference V

Examples: 1. Find the power output by a flashlight bulb drawing 0.3 A from a 1.5 V cell. 2. Find the current drawn by a 500 W resistor when connected to 120 V.

Other Versions of the Power Rule V IR Also from Ohm s Law. Thus P VI becomes: P VI Also V I R from Ohm s Law. Thus P VI becomes:

Examples: 1. What is the resistance of a 1500 W hair dryer that draws a current of 13 A? 2. What is the power rating on a light bulb with a resistance of 2 W, that is connected to 120 V AC?

3. What is the power dissipated through the following resistors at 12 V DC? (a) 15 W (b) 50 W (c) 150 W (d) 300 W Which one would becomes the hottest? Hint: It is the one that has the highest wattage. Which one draws the most current?

V 0 R 0 I 0 Power Rules for Series Circuits Consider V 1 R 1 I 1 V 3 R 3 I 3 TP P1 P2 P3 0 0 0 0 V 2 R 2 I 2 But, So, V V V V 0 1 2 3 P V I TP P1 P2 P3 I I I I 0 1 2 3 And ALL of the currents are equal Multiply by I 0 TP P1 P2 P3 I I I I

Thus, to find the total power of a series circuit simply add ALL of the powers together

Power Rules for Parallel Circuits Consider V 0 R 0 I 0 V 1 R 1 I 1 V 2 R 2 I 2 V 3 R 3 I 3 TP P1 P2 P3 0 0 0 0 But, So, I I I I 0 1 2 3 P I V TP P1 P2 P3 V V V V 0 1 2 3 And ALL of the voltages are equal Multiply by V 0 TP P1 P2 P3 V V V V

Thus, to find the total power of a parallel circuit simply add ALL of the powers together In fact if there is a hybrid circuit containing both parallel and series branches, you simply add ALL of the powers together to find the total power!

V 0 =120v Examples. 1. Find the total current. P 1 60 W P 2 =100 W P 3 = 60 W

V 0 = 120 V 2. Complete the table for circuit below P 1 = 60 W P 2 = 100 W P 3 =100 W P 4 = 100 W P 1 P 2 P 3 P 4 P 0 V I R

Cost of Electricity Electrical energy is measured in kilowatt hours. Definition: 1 kwh is the energy dissipated in 1 hour by a load with a power of 1 kw. Formula: E = Pt C = Er (for Energy) (for Cost (C) at a rate of r cents/kwh)

Example 1 If power costs 10.064 /kwh, how much does it cost for a 100 W bulb to light a room for: A) a day B) a year C) 18 years

Example 2 Find the cost of cooking a turkey for 5 hours in an oven that draws 15 A of current from a 240 V supply at a rate of 10.064 / kwh.