Physics 104: Lecture 5

1
Physics 104 Lecture 5

• Resistance
• Electric Power
• EMF Internal Resistance
• DC Resistor Circuits
• Resistors in Series and Parallel
• Circuit Analysis
• Electrical Hazards

2
Electric Terminology

• Current Moving Charges
• Symbol I
• Unit Amp ? Coulomb/second
• Count number of charges which pass point/sec
• Power Energy/Time
• Symbol P
• Unit Watt ? Joule/second Volt Coulomb/sec
• PW/?tVq/?t VI

3
Resistance

• In a conductor, the voltage applied across the
  ends of the conductor is proportional to the
  current through the conductor. ?VRI
• The constant of proportionality is the resistance
  of the conductor
• Units of resistance are ohms (?)
• 1 ? 1 V / A

4
Physical Resistor

• Resistance Traveling through a resistor,
  electrons bump into things which slows them down.
  R r L /A
• r Resistivity Density of bumps
• L Length of resistor
• A Cross sectional area of resistor
• Ohms Law I V/R
• Double potential difference ?double current
• I (VA)/ (r L)

A
L
5
Preflight 1

• Two cylindrical resistors are made from the same
  material. They are of equal length but one has
  twice the diameter of the other.
• R1 gt R2
• R1 R2
• R1 lt R2

2
1
Smaller diameter ? not as easy for stuff to flow
through
6
Resistance vs Temperature

• Resistance depends on
• Collisions in the material medium
• Availability of free charges in material
• Temperature dependence of resistance
• The rate of collision of free charges with atoms
  depends on the temperature
• Higher the temperature the greater atomic
  vibration that increases collision probability.
  Higher resistance.
• Number of free charges available in a material
  can depend on temperature
• Electrons can be freed from their orbits around
  nuclei. Lower resistance.

7
Resistivity, Resistance vs. Temp.

• For most metals, resistivity increases
  approximately linearly with temperature over a
  limited temperature range
• ?
• ??? is the resistivity at some temperature T
• ???o is the resistivity at some reference
  temperature To
• To is usually taken to be 20 C
• ? is the temperature coefficient of resistivity
• Since the resistance of a conductor with uniform
  cross sectional area is proportional to the
  resistivity, you can find the effect of
  temperature on resistance

8
Metals

• At room temperature metals have several free
  electrons per atom
• Resistivity varies with temperature linearly due
  to increasing probability of collisions with
  atoms

9
Semiconductors

• At room temperature pure semiconductors have few
  free electrons
• With increasing temperature electrons are freed
  from atomic orbits
• Resistance decreases with temperature

10
Super-conductors

• At very low temperatures resistance can drop to
  zero abruptly - phase transition

11
Energy Transfer in the Circuit

• Imagine a quantity of positive charge, DQ, moving
  around the circuit from point A back to point A
• As the charge moves through the battery from A to
  B, the potential energy of the system increases
  by DQDV
• As the charge moves through the resistor, from C
  to D, it loses energy in collisions with the
  atoms of the resistor

12
Electrical PowerPower Dissipated in a resistor

• Electric energy depends on both voltage drop and
  charge moved

• The SI unit of power is Watt (W)
• I must be in Amperes, R in ohms and DV in Volts
• Unit of energy used by electric companies is
  the kilowatt-hour E Pt
• Defined in terms of the unit of power and
  amount of time it is supplied
• 1 kWh 3.60 x 106 J

13
emf Internal Resistance

• The source that maintains the current in a closed
  circuit is called a source of emf
• Devices that increase the potential energy of
  charges circulating in circuits are sources of
  emf
• Examples batteries generators
• Emf is work done per charge
• V W/q, W-gtPE
• SI units are Volts
• Real battery has some internal resistance
• Therefore, the terminal voltage is not equal to
  the emf

14
Internal Resistance

• Terminal volts ?V Vb-Va
• ?V e Ir
• For the entire circuit,e IR Ir
• e equals terminal voltagewhen current is zero
• open-circuit voltage
• When R gtgt r, r can be ignored
• Generally assumed in problems unless otherwise
  stated
• Power relationship PI e I2 R I2 r
• When R gtgt r, most of the power delivered by the
  battery is transferred to the load resistor

Internal resistance?
Load resistance?
15
Resistors in Series

• One wire
• Effectively adding the lengths
• Since R a L add resistance Reqr(L1L2)/A

• - If charge goes through one resistor, it must go
  through other.
• - I1 I2 Ieq
• V1 V2 Veq
• R1 R2 Req

16
Question?
R11W
V0

• Compare V1 the voltage across R1, with V10 the
  voltage across R10.
• V1ltV10
• V1V10
• V1gtV10

R1010W
V I R, I the same through both resistors V1
I1 R1 I V10 I10 R10 10 I
17
Resistors in Parallel

• Two wires
• Effectively adding the Area
• Since R a 1/A add 1/R
• Both ends of resistor are connected
• I1 I2 Ieq
• V1 V2 Veq
• 1/Req 1/R1 1/R2

29
18
Preflight 6

• What happens to the current through resistor 2
  when the switch is closed?
• Increases
• Remains Same
• Decreases

• Follow UpWhat happens to the current through the
  battery?
• Increases
• Remains Same
• Decreases

Ibattery I2 I3
19
Example
e
Calculate current through each resistor. R1 10
W, R2 20 W, R3 30 W, e44 V

• Simplify R2 and R3 are in parallel
• 1/R23 1/R2 1/R3
• V23 V2 V3
• I23 I2 I3

R23 12 W

• Simplify R1 and R23 are in series
• R123 R1 R23
• V123 V1 V23 e
• I123 I1 I23 Ibattery

R123 22 W
I123 44 V/22 W 2 A
Power delivered by battery
PIV 2?44 88W
20
Ammeters Voltmeters

• Ammeters measure current
• In line with the bulb, all the charge passing
  through the bulb also must pass through the meter
• Voltmeters measure voltage (potential diff.)
• Connects to the two ends of the bulb

21
Last Week

• Capacitors
• Physical C e0A/d
• Series 1/Ceq 1/C1 1/C2
• Parallel Ceq C1 C2
• Energy PE 1/2 QV

Today

• Resistors
• Physical R r L/A
• Series Req R1 R2
• Parallel 1/Req 1/R1 1/R2
• Power P IV

22
Resistance Summary
Resistance R r L/A
Ohms Law I ? V
Power Dissipated P V I I2 R
Series
Parallel
R1
R1
R2
R2
Same for each resistor. Vtotal V1 V2
Different for each resistor. Vtotal V1 V2
Voltage
Different for each resistor Itotal I1 I2
Same for each resistor Itotal I1 I2
Current
Resistance
Increases Req R1 R2
Decreases 1/Req 1/R1 1/R2
23
Electrical Hazards

• Thermal hazard
• Too many appliances on an outlet, in parallel -
  large current - over heating (I2R) - fire
• Fuse saves you
• Circuit breaker
• Bimetallic strip that disconnects on over heating
• Shock hazard
• The amount of current, I
• Path taken
• Duration
• Frequency (power not constant for AC)

24
Extra
25
Question

• An electric shock due to a 10000V potential
  difference is always fatal
• True
• False

Static shocks (conduction through air to door
knob) Dielectric strength of air 3 x 106
V/m Voltage difference for 1 cm gap to knob
30000 V
26
Temperature Resistance

• For most metals, resistivity increases with
  increasing temperature
• With a higher temperature, the metals atoms
  vibrate with increasing amplitude electrons find
  it more difficult to pass through the atoms

27
Simple Circuit
I
V
R
I

• Example
• Calculate I when V24 Volts and R 8 W
• Ohms Law VIR
• I V / R 24 V / 8 W 3 A

28
Resistors in Series

• One wire
• If charge goes through one resistor, it must go
  through other.
• I1 I2 Ieq
• V1 V2 Veq
• Add Req R1 R2
• Adding Voltage IR1 IR2I(R1 R2)
• Adding length Reqr(L1L2)/A

R1
Req
R2
29
Series Example
R11W

• Calculate the voltage across each resistor if the
  battery has potential V0 22 volts.

V0
R210W

• R12 R1 R2
• V12 V1 V2
• I12 I1 I2

Simplify R1 and R2 are in series
11 W
V0 22 Volts
V12/R12 2 Amps

• Expand
• V1 I1R1
• V2 I2R2

2 x 1 2 Volts
R11W
2 x 10 20 Volts
V0
Check V1 V2 V12
R210W
30
Resistors in Parallel

• Two wires
• Both ends of resistor are connected
• I1 I2 Ieq
• V1 V2 Veq

• Add 1/Req 1/R1 1/R2
• Adding Current V/R1V/R2V(1/R11/R2)
• Adding Area

32
31
Question?

• As more and more resistors are added to the
  parallel resistor circuit shown here the total
  resistance between the points P and Q
• Increases
• Remains the same
• Decreases

32
Johnny Danger Powells uses one power strip to
plug in his microwave, coffee pot, space heater,
toaster, and guitar amplifier all into one
outlet. This is dangerous because (By the way,
power strips are wired in parallel.)
Toaster
PVI gets too large - burns wire
33
Preflight 1
R11W

• Compare I1 the current through R1, with I10 the
  current through R10.
• I1ltI10
• I1I10
• I1gtI10

V0
R1010W
The current will remain constant throughout the
circuit--because there is no where else for the
current to go.
34
Parallel Example
e
R2
R3

• Determine the current through the battery.
• Let E 60 Volts, R2 20 W and R330 W.

Simplify R2 and R3 are in parallel
1/R23 1/R2 1/R3 V23 V2 V3 I23 I2 I3
R23 12 W
e
R23
60 Volts
V23 /R23 5 Amps
35
Preflight 5-8
1
2
3
R 2R R/2

• Which configuration has the smallest resistance?
• 1
• 2
• 3

Which configuration has the Largest
resistance? 1 2 3
36
Example
Calculate current through each resistor. R1 10
W, R2 20 W, R3 30 W, e44 V

• Expand R1 and R23 are in series
• R123 R1 R23
• V123 V1 V23 e
• I123 I1 I23 Ibattery

I23 2 A
V23 I23 R23 24 V

• Expand R2 and R3 are in parallel
• 1/R23 1/R2 1/R3
• V23 V2 V3
• I23 I2 I3

I2 V2/R2 24/201.2A
e
I3 V3/R3 24/300.8A
37
Electrical Energy Power

• The rate at which the energy is lost is the
  power
• From Ohms Law, alternate forms of power are
• The SI unit of power is Watt (W)
• I must be in Amperes, R in ohms and DV in Volts
• Unit of energy used by electric companies is the
  kilowatt-hour
• Defined in terms of the unit of power and amount
  of time it is supplied
• 1 kWh 3.60 x 106 J