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Current Resistance

6th Edition Chapter 27

- Chapter 26

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

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

Electric Current

- A loop of copper wire with no battery ? no

current - With a battery ? electric field ? current

Electric Current

- The current I through the conductor has the same

value at all the planes. Why?

Electric Current

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

- Charge is conserved
- i0 i1 i2

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

Current Density

If the current density is uniform and parallel to

the area vector

Checkpoint 1

What is the magnitude and direction of the

current i in the lower right-hand wire?

Drift Speed

Resistance

Units of resistance is 1 ohm 1 O 1 volt per

ampere 1 V/A

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

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?

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?

Resistivity

Resistivity ? of a material is defined as (units

O.m)

Or in vector form

Conductivity

Conductivity is the reciprocal of resistivity

Or in vector form

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

Checkpoint 3

Rank these according to the current through them,

greatest first, when the same potential

difference V is placed across their lengths.

Variation of ? with Temperature

Variation of ? with Temperature

- ?0 1.6910-8 O.m
- T0 293 K (room T)

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

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.

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)

Ohms Law

- When the resistivity of the material changes with

the applied electric field the material does not

obey Ohms law. (Non-constant slope)

Power in Electric Circuits

- Electric power is the rate of electrical energy

transfer

Power in Electric Circuits

- Using the definition of R (RV/i)

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.

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?

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?

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?

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.

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?

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?

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?

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?

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