Ch 18 1

Chapter 18Electric Currents

Ch 18 2

Simple Electric Cell

Sulfuric acid

Zn+ Zn+

Zn+ Zn+

+++

___

Carbon Electrode

(+)

Zn Electrode(-)

•Two dissimilar metals or carbon rods in acid

•Zn+ ions enter acid leaving terminal negative

•Electrons leave carbon making it positive

•Terminals connected to external circuit

•‘Battery’ referred to several cells originally

Ch 18 3

Electric Current

•If we connect a wire between the two terminals electrons will flow out of the negative terminal and toward the positive terminal we have an electric current.•Electric current I is defined as the net amount of charge that flows past a given point per unit time.

t

QI

1 C/s = 1A (ampere)•An ampere is a large current and often currents are mA (10-3 A) or A (10-6 A).

Ch 18 4

Electric Circuit• It is necessary to have a complete circuit in order for

current to flow.

• The symbol for a battery in a circuit diagram is:

+ _

Device

+

Ch 18 5

“Conventional” current direction is opposite to actual electron flow direction which is – to +.

Ch 18 6

Ohm’s Law• For wires and other circuit devices, the current is proportional to the voltage applied to its ends:

I V• The current also depends on the amount of resistance that the wire offers to the electrons for a given voltage V. We define a quantity called resistance R such that

V = I R (Ohm’s Law)• The unit of resistance is the ohm which is represented by the Greek capital omega ().• Thus

A

V1

Ch 18 7

Resistors• A resistor is a circuit device that has a fixed resistance.

Resistor

Circuit symbol

Resistors obey Ohm’s law but not all circuit devices do (semi-conductor diode, LED)

I

V0

I

V0

Resistor non-ohmic device

Ch 18 8

Example: A person experiences a mild shock if a current of 80 A flows along a path between the thumb and the index finger. The resistance of this path is 4.0x105 when the skin is dry and 2000 when the skin is wet. Calculate the minimum voltage difference between these two points that will produce a mild shock.

Ch 18 9

Example: A person experiences a mild shock if a current of 80 A flows along a path between the thumb and the index finger. The resistance of this path is 4.0x105 when the skin is dry and 2000 when the skin is wet. Calculate the minimum voltage difference between these two points that will produce a mild shock.

RIV

V

AVDRY

32

100.41080 56

V

AVWET

16.0

100.21080 36

Ch 18 10

Example: Calculate the number of electrons per second that flow past a point on the skin in the previous example.

Ch 18 11

Example: Calculate the number of electrons per second that flow past a point on the skin in the previous example.

t

QI

sec100.5 14 electrons

electroncharge

sec

#

tQelectrons

C

electron

t

Q19106.1

1

C

electrons

C19

6

106.1

11080

Ch 18 12

Power in Electric Circuits

• Electrical circuits can transmit and consume energy.

• When a charge Q moves through a potential difference V, the energy transferred is QV.

• Power is energy/time and thus:

VI

and thus:

IVP

time

energypowerP

t

QV V

t

Q

Ch 18 13

Notes on Power

wattWs

J

C

J

s

CVIP

•The formula for power applies to devices that provide power such as a battery as well as to devices that consume or dissipate power such as resistors, light bulbs and electric motors.

•For ohmic devices, the formula for power can be combined with Ohm’s Law to give other versions:

RIRIIVIP 2)(

R

VV

R

VVIP

2

Ch 18 14

Household Power•Electric companies usually bill by the kilowatt-hour (kWh.) which is the energy consumed by using 1.0 kW for one hour.

•Thus a 100 W light bulb could burn for 10 hours and consume 1.0 kWh.

•Electric circuits in a building are protected by a fuse or circuit breaker which shuts down the electricity in the circuit if the current exceeds a certain value. This prevents the wires from heating up when carrying too much current.

Ch 18 15

Connection of

Household Appliances

Ch 18 16

Example: A person turns on a 1500 W electric heater, a 100 W hair dryer and then a 300 W stereo. All of these devices are connected to a single 120 V household circuit that is connected to a 20 A circuit breaker. At what point will the circuit breaker trip off?

Ch 18 17

Example: A person turns on a 1500 W electric heater, a 100 W hair dryer and then a 300 W stereo. All of these devices are connected to a single 120 V household circuit that is connected to a 20 A circuit breaker. At what point will the circuit breaker trip off?

dryerwithtrips

breakerCircuit

VIP

AV

WI

dryer3.8

120

1000

AV

WI

bulb83.0

120

100

AV

WI

heater5.12

120

1500

V

PI

AV

WI

stereo5.2

120

300

Ch 18 18

Example: If electricity costs $0.1379 per kWh in Nova Scotia, calculate the cost of operating all the appliances in the previous problem for 2.0 hours.

Ch 18 19

Example: If electricity costs $0.1379 per kWh in Nova Scotia, calculate the cost of operating all the appliances in the previous problem for 2.0 hours.

cos 1.5 2 $0.1379

$ 0.41

Heater t kW h kWh

$ 0.083

$0.80

Stereo

$ 0.28Dryer

$ 0.028Bulb

Ch 18 20

Microscopic View of Current•Read Example 18-13 on page 545. It studies a 5.0A current in a copper wire that is 3.2 mm in diameter. It finds that the average “free” electron moves with a velocity of 4.7 x 10-5 m/s in the direction of the current. This is called the drift velocity.

•It also assumes the “free” electrons behave like an ideal gas and calculates that the thermal velocity of the average electron is 1.2 x 105 m/s.

•Thus in a wire carrying a current, the electron motion is largely random with a slight tendency to move in the direction of the current. Thus if you could see electrons in a wire carrying current they would appear to be moving randomly.

Ch 18 21

Summary of Units

Ch 19 22

Chapter 19DC Circuits

Ch 19 23

EMF

• Devices that supply energy to an electric circuit are referred to as a source of electromotive force. Since this name is misleading, we just refer to them as source of emf (symbolized by and a slightly different symbol in the book.)

• Sources of emf such as batteries often have resistance which is referred to as internal resistance.

Ch 19 24

Terminal Voltage

r a b

Vab

•We can treat a battery as a source of in series with an internal resistor r.•When there is no current then the terminal voltage is Vab= •But with current I we have:

r Vab

•The internal resistance is small but increases with age.

Ch 19 25

Circuit Symbols

Ch 19 26

Resistors in Series - Derivation

•We want to find the single resistance Req that has the same effect as the three resistors R1, R2, and R3.•Note that the current I is the same throughout the circuit since charge can’t accumulate anywhere.•V is the voltage across the battery and also

V = V1 + V2 + V3

•Since V1 = I R1 etc., we can say321321 IRIRIRVVVV

)( 321 RRRIV The equivalent equation is V=IReq and thus

321 RRRReq

Ch 19 27

Summary - Resistors in Series

The current I is the same throughout the circuit since charge can’t accumulate anywhere.

321 RRRReq

321 VVVV

Ch 19 28

Resistors in Parallel - Derivation

This is called a parallel circuit•Notice V1 = V2 = V3 = V•Since charge can’t disappear, we can say

321

1111

RRRReq

332211321 RVRVRVIIII

•We can combine these equations with V = IReq to give

Ch 19 29

Summary - Resistors in Parallel

•The electric potential (voltage) is the same across each resistor

V1 = V2 = V3

•The current through the battery splits several ways I = I1 + I2 + I3

•Can be 2, 3 or more resistors in parallel.

321

1111

RRRReq

Ch 19 30

Example: A 3.0 V battery is connected to three resistors as shown. Calculate the resistance of the equivalent circuit and the power dissipated in the equivalent circuit. R1 = 500 Ω, R2 = 1000 Ω and R3 = 2000 Ω.

Ch 19 31

321

1111

RRRREQ

2000

1

1000

1

500

1

286EQR

EQRIV

EQR

VI

286

00.3 VmA5.10

VIP )00.3()5.10( VmA

mWP 5.31

Example: A 3.0 V battery is connected to three resistors as shown. Calculate the resistance of the equivalent circuit and the power dissipated in the equivalent circuit. R1 = 500 Ω, R2 = 1000 Ω and R3 = 2000 Ω.

Ch 19 32

Example: From the previous example, calculate the current and the power dissipated in each resistor and the total power dissipated in the circuit.

Ch 19 33

Example: From the previous example, calculate the current and the power dissipated in each resistor and the total power dissipated in the circuit.

RIV

11 R

VI

500

00.3 V mA0.6

111 VIP )00.3()0.6( VmA mW0.18

22 R

VI

1000

00.3 VmA0.3

222 VIP )00.3()0.3( VmA mW0.9

33 R

VI

2000

00.3 V mA5.1

333 VIP )00.3()5.1( VmA mW5.4

321 IIII mA5.10

321 PPPP mW5.31

Ch 19 34

Example: A 3.0 V battery is connected to 4 resistors as shown. Calculate the resistance of the equivalent circuit and the current in the equivalent circuit. R1 =

500 Ω, R2 = 1000 Ω, R3 = 1000 Ω, and R4 = 2000 Ω.

Ch 19 35

seriesinareRandR 32

3223 RRR 10001000

200023R

parallelinareRandR 423

423324

111

RRR

2000

1

2000

1

1000234RseriesinareRandR 2341

2341 RRREQ 1000500 1500

RIV

EQR

VI

1500

0.3 VmA0.2

Example: A 3.0 V battery is connected to 4 resistors as shown. Calculate the resistance of the equivalent circuit and the current in the equivalent circuit. R1 =

500 Ω, R2 = 1000 Ω, R3 = 1000 Ω, and R4 = 2000 Ω.

Ch 19 36

Ammeter

•To measure current ammeter must be connected in series.

•Must have small internal resistance or it will reduce current and give a faulty measurement.

Ch 19 37

Voltmeters

•To measure voltage difference, it must be connected in parallel.

• Must have high internal resistance or it will draw too much current which reduces voltage difference and gives a faulty measurement.