Chapter 27 Ohms Law

1
Chapter 27 Ohms Law

• PHYS 2326-13

2
Concepts to Know

• Current
• Drift Velocity
• Concentration of Particles
• Current Density
• Resistivity
• Resistance
• Temperature Coefficient of Resistivity
• Electric Power

3
Current Density

• Current density is the current per unit area
  traveling through a cross sectional area A.
• J I/A Amperes/meter squared
• Valid for cross section perpendicular to the
  direction of travel and for uniform current
  density.
• J s E where sigma is the conductivity of the
  conducting material (not valid for all materials)
  For those where valid Ohms Law

4
Ohms Law

• Jn q vd where n is the free electrons/m3 , vd
  is the drift velocity and q is the charge per
  electron,
• I n q vd A where A is the cross sectional area
  perpendicular to the current flow
• V El when a small V is applied between the ends
  of a wire of length l
• J sE sV/l or E J/ s 1/ s ?
• sigma is conductivity not charge density

5
Ohms Law

• ?V (l / s) J (l / (s A) ) I R I
• R ?V/I
• R resistance Ohm (O) 1 Volt/Ampere
• s conductivity 1/? (rho) resistivity
• R ? (l / A)
• bulk property increases with length, decreases
  with cross sectional area
• resistivity function of material and of
  temperature

6
Resistors

• Resistors are components designed to have a
  particular value. Typically, these have a color
  code with value and multipliers. BBROYGBVGW is
  0-9 or 1,10,100, . 109, Gold silver none are
  5, 10 and 20 for the old ones. Standard
  values are a bit odd as theyre based upon
  accuracy ranges. Modern ones are typically 5 2
  1 or better

7
Resistor Types

• Carbon film most common now
• Carbon composition becoming rare but is best
  under surge conditions like nearby lightning
• Other common types wire wound, precision metal
  film
• Platinum RTD (resistance temperature devices) are
  very high precision temperature measurement
  sensors.

8
Resistance Temperature Coefficient

• Resistivity
• ? ? o (1 a (T-To ) )
• a (alpha) is temperature coefficient of
  resistivity
• Since resistance is proportional to resistivity
• RRo (1 a (T-To ) )

Resistance schematic symbol
9
Electrical Power

• Power dissipation in a resistor
• dU/dt d/dt (Q?V) dQ/dt ?V I ?V
• U energy, I current
• Power P delivered to resistor I ?V
• Often E symbol used for V so we have PIE
• Using Ohms law IV/R
• P I2 R (?V) 2/R
• Power is Watts Joules / second

10
Example 1

• Given copper wire 1mm dia. 100m long has a
  potential diff. of 12 V
• Find a) resistance, b) current in wire, c)
  current density, d) electric field in wire, e)
  concentration of electrons (assuming 1 / atm), f)
  drift velocity, g) amount of electric charge
  flowing in 1 minute

11
Example 1

• ? 1.72E-8 Ohm-m resistivity
• D 8.9 E 3 kg/m3 density
• M 63.546 g/mole molecular weight
• avagadros 6.022E 23
• e 1.6E-19 C electric charge
• r 5E-4m radius, L100m, t60sec

12
Example 1

• Equations Answers
• R ?L/A, Apr2 A7.85E-7, R2.19 O
• VIR IV/R 5.48 A
• JI/A J6.977E6 A/m2
• E ?J 0.12 V/m
• n D Na /M 8.434E28 e/m3
• I n q vd A vd I/nqA 5.17E-4 m/s
• I dQ/dt Q It 329 C

13
Example 2

• 100 W light bulb connected to 110V what is a)
  current b) resistance c) at 10cents/kwhour how
  much to illuminate for a year, d) how many can be
  connected to a 15 ampere circuit breaker, e) how
  much electric power consumed by all these bulbs,
  f) if the temperature is 4500K and made from
  tungsten (a 0.0038/K) what is the room
  temperature resistance at 300K

14
Example 2

• Given P100 W, V 100V Imax 15A
• c 0.1 /kW h T4500 K To 300 K
• a 0.0038/K
• Equations Answers
• P IV IP/V 0.909 A
• V IR RV/I 121 O
• cost (0.1)(.1KW)(24365) 87.60
• Imaxgt Nmax I Nmax 16
• Pmax Nmax P Pmax 1600W
• RRo(1 a (T-To)) Ro 7.13 O

15
Resistance Circuits

• I ?V/R ?V Va-Vb
• Parallel Series
• 1/R I/?V R ?Vx/I
• I I1 I2 I3 ?V ?V1?V2?V3

Vb
Va
Va
Vb
Parallel Series 1/Rt 1/R1 1/R2 1/R3
Rt R1R2R3
16
Example 3

• Combine Series R1 R2 toR5
• Combine Parallel 1/R5 1/R4 1/R6
• Combine Series R6 R3 R7

R2
R6
c
R1
a
Ro
R4
Ro
R3
R5
R3
b
R4
Ro
R7
R3
17
Example 3

• Given Ro 1 O, R1 1O, R2 2 O, R3 3 O
• R4 6 O, Vo 12V Find a) voltage across and
  current through each resistor, b) voltage Vab
  across the battery, c) the electric potential at
  point c.
• Find equivalent resistance and work backwards to
  get voltage and current

18
Example 3

• R5 R1R2 12 3 O
• R4 R5 parallel 1/R6 1/R4 1/R5 2 O
• Ro, R6 R3 in series, R7 RoR6R3 6 O
• V IR7, IV/R 2A
• Io I3 I6 I
• Vo IoRo 2 V
• V3 I3 R3 6V
• V6 I6 R6 4V
• V5 V6 I5 R5, I5 1.333A
• V4 V6 I4 R4, I4 0.667A
• I2 I5, V2I2 R2, V2 2.667V

19
Example 3

• a) Vo 2 V Io 2 A
• V1 1.333 V I1 1.333 A
• V2 2.667 V I2 1.333 A
• V3 6 V I3 2 A
• V4 4V I4 0.667A
• b) Vab V Vo 10V
• c) Vc Vcb V2V3 8.667V