Current

1
Current Resistance
6th Edition Chapter 27

• Chapter 26

2
Chapters Main Idea

• Basic definitions
• Current, Current Density, Drift Speed
• Calculating the resistance of a conductor and the
  effect of temperature on it.
• Ohms Law
• Power

3
Moving Charges Electric Current

• An electric current is a stream of charges.
• This chapter is studying

Steady currents of conduction electrons moving
through metallic conductor such as copper wires
4
Electric Current

• A loop of copper wire with no battery ? no
  current
• With a battery ? electric field ? current

5
Electric Current

• The current I through the conductor has the same
  value at all the planes. Why?

6
Electric Current

• Units of current is ampere
• 1 ampere 1 A 1 1 C/s

• Charge is conserved
• i0 i1 i2

7
Direction of Current

• A current arrow is drawn in the direction in with
  positive charge would move, even if the actual
  charge carriers are negative and move in the
  opposite direction

8
Current Density
If the current density is uniform and parallel to
the area vector
9
Checkpoint 1
What is the magnitude and direction of the
current i in the lower right-hand wire?
10
Drift Speed
11
Resistance
Units of resistance is 1 ohm 1 O 1 volt per
ampere 1 V/A
12
Checkpoint 2
What is the direction of (a) the current i, (b)
the current density J, and (c) the electric field
E in the wire
13
Sample Problem 2

• (a) The current density in a cylindrical wire of
  radius R2.00 mm is uniform across a cross
  section of the wire and is given by J 2.0105
  A/m2. What is the current through the outer
  portion of the wire between radial distances R/2
  and R?
• (b) Assume that the current density is given by
  Jar2, in which a31011 A/m4. What now is the
  current through the same portion?

14
Sample Problem 3

• One end of an aluminum wire whose diameter is 2.5
  mm is welded to one end of a copper wire whose
  diameter is 1.8 mm. The composite wire curries a
  steady current I of 17 mA.
• What is the current density in each wire?
• What is the drift speed of the conduction
  electrons in the copper wire?

15
Resistivity
Resistivity ? of a material is defined as (units
O.m)
Or in vector form
16
Conductivity
Conductivity is the reciprocal of resistivity
Or in vector form
17
Calculating R from ?
For this wire the electric field E and current
density J are given by
Using the definition of R that R V/i
The resistivity ? is the ratio of E to J
18
Checkpoint 3
Rank these according to the current through them,
greatest first, when the same potential
difference V is placed across their lengths.
19
Variation of ? with Temperature
20
Variation of ? with Temperature

• ?0 1.6910-8 O.m
• T0 293 K (room T)

21
Sample Problem 6

• A rectangular block of iron has dimensions 1.2 cm
  x 1.2 cm x 15 cm.
• What is the resistance of the clock measure
  between the two square ends?
• What is the resistance between two opposite
  rectangular faces

22
Ohms Law

• Ohms law is an assertion that the current
  through a device is always directly proportional
  to the potential difference applied to the device.

23
Ohms Law

• A conducting material obeys Ohms law when the
  resistivity of the material is independent of the
  magnitude and direction of the applied field
  (constant slope on the i-V graph)

24
Ohms Law

• When the resistivity of the material changes with
  the applied electric field the material does not
  obey Ohms law. (Non-constant slope)

25
Power in Electric Circuits

• Electric power is the rate of electrical energy
  transfer

26
Power in Electric Circuits

• Using the definition of R (RV/i)

27
Checkpoint 5
A potential difference V is connected across a
resistance R, causing current I through the
resistance. Rank the following variations
according to the change in the rate at which
electrical energy is converted to thermal energy
in the resistance, greatest change first (a) V
is doubled with R unchanged, (b) i is doubled
with R unchanged, (c) R is doubled with V
unchanged, (d) R is doubled with i unchanged.
28
Sample Problem 8

• A wire of length L2.35 m and diameter d1.63 mm
  carries a current i of 1.24 A. The wire
  dissipates electrical energy at the rate P of
  48.5 mW. Of what material is the wire made?

29
Problem Set 6 Q1

• A current of 3.6 A flows through an automobile
  headlight. How many coulombs of charge flow
  through the headlight in 3.0 h?

30
Problem Set 6 Q2

• When a wire carries a current of 1.20 A, the
  drift velocity is 1.20 X 10-4 m/s. What is the
  drift velocity when the current is 6.00 A?

31
Problem Set 6 Q3

• In household wiring, copper wire 2.05 mm in
  diameter is often used. Find the resistance of a
  24.0-m length of this wire.

32
Problem Set 6 Q4

• You apply a potential difference of 4.50 V
  between the ends of a wire that is 2.50 m in
  length and 0.654 mm in radius. The resulting
  current through the wire is 17.6 A. What is the
  resistivity of the wire?

33
Problem Set 6 Q5

• A certain resistor has a resistance of 1.484 O at
  20.0C and a resistance of 1.512 O at 34.0C.
  What is its temperature coefficient of
  resistivity?

34
Problem Set 6 Q6

• The open-circuit terminal voltage of a battery is
  12.6 V. When a resistor R 4.00 O is connected
  between the terminals of the battery, the
  terminal voltage of the battery is 10.4 V. What
  is the internal resistance of the battery?

35
Problem Set 6 Q7

• A resistor with a 15.0-V potential difference
  across its ends develops thermal energy at a rate
  of 327 W. a) What is its resistance? b) What is
  the current in the resistor?