Physics 1202: Lecture 7Today’s Agenda

• Announcements:– Lectures posted on:

www.phys.uconn.edu/~rcote/

– HW assignments, solutions etc.

• Homework #2:Homework #2:– On Masterphysics today: due Friday weekOn Masterphysics today: due Friday week

– Go to masteringphysics.com

• Labs: Begin THIS week

Today’s Topic :• Electric current (Chap.17)

• Review of– Electric current– Resistance

• New concepts– Temperature dependence– Electromotive force (battery)– Power– Circuits

» Devices» Resistance in series & in parallel

R

I

= R I

Current Idea

Current is the flow of charged particles through a path, at circuit.

Along a simple path current is conserved, cannot create or destroy the charged particles

Closely analogous to fluid flow through a pipe. Charged particles = particles of fluid

Circuit = pipes

Resistance = friction of fluid against pipe walls, with itself.

E

Ohm's Law

• Vary applied voltage V.

• Measure current I

• Does ratio ( V/I ) remain constant??

V

I

slope = R = constant

V

I IR

Resistivity

LA

E

j

e.g, for a copper wire,

~ 10-8 -m, 1mm radius, 1 m long, then R .01

So, in fact, we can compute the resistance if we know a bit about the device, and YES, the property belongs only to the device !

Make sense?

LA

E

j

• Increase the Length, flow of electrons impeded

• Increase the cross sectional Area, flow facilitated

• The structure of this relation is identical to heat flow through materials … think of a window for an intuitive example

How thick?

How big?

What’s it made of?

or

Lecture 7, ACT 1• Two cylindrical resistors, R1 and R2, are made of identical material.

R2 has twice the length of R1 but half the radius of R1. – These resistors are then connected to a battery V as shown:

VI1 I2

– What is the relation between I1, the current flowing in R1 , and I2 , the current flowing in R2?

(a) I1 < I2 (b) I1 = I2 (c) I1 > I2

Lecture 7, ACT 2

R

I

1

2 3

4

+

-

x

1 2 3 4

+-

1 2 3 4

+-

1 2 3 4

+-

Consider a circuit consisting of a single loop containing a

battery and a resistor.

Which of the graphs represents

the current I around the loop?

Conductivity versus Temperature• In lab you measure the resistance of a light bulb

filament versus temperature.

• You find RT.

• This is generally (but not always) true for metals around room temperature.

• For insulators R1/T.

• At very low temperatures atom vibrations stop. Then what does R vs T look like??

• This was a major area of research 100 years ago – and still is today.

temperature coefficient of resistivity

Electromotive force• Provides a constant potential difference between

2 points : “electromotive force” (emf)

R

I I

rV

+ -

• May have an internal resistance– Not “ideal” (or perfect: small loss of V)

– Parameterized with “internal resistance” r in series with

• Potential change in a circuit

- Ir - IR = 0

Power• Battery:

Stores energy chemically. When attached to a circuit, the energy is transferred to the motion of electrons. This happens at a constant potential.» Battery delivers energy to a circuit.

» Other elements, like resistors, dissipate energy. (light, heat, etc.)

• Total energy delivered not always useful.– How much energy does it take to light your house

… well for how long?

– Remember definition of Power (Phys. 1201).

Power• Recall that

• In a circuit, where the potential remains constant.– Only q varies with time

where

PowerBatteries & Resistors Energy expended

What’s happening?

Assert:

chemical to electrical

to heat

Charges per time

Energy “drop” per charge

Units okay?

For Resistors:

Rate is:

Power

• What does power mean?– Power delivered by a battery is the amount of

work per time that can be done. i.e. drive an electric motor etc.

– Power dissipated by a resistor, is amount of energy per time that goes into heat, light, etc.

• A light bulb is basically a resistor that heats up. The brightness (intensity) of the bulb is basically the power dissipated in the resistor.– A 200 W bulb is brighter than a 75 W bulb, all

other things equal.

Batteries (non-ideal)• Parameterized with

“internal resistance” r in series with

• : “electromotive force” (emf)

R

I I

rV

Power delivered to the resistor R:

Pmax when R/r =1 !

= V(I=0)

- Ir - IR = 0

- Ir = V

R

I

= R I

Devices• Conductors:

Purpose is to provide zero potential difference between 2 points. » Electric field is never exactly zero.. All conductors

have some resistivity.

» In ordinary circuits the conductors are chosen so that their resistance is negligible.

• Batteries (Voltage sources, seats of emf):

Purpose is to provide a constant potential difference between 2 points. » Cannot calculate the potential difference

from first principles.. electrical chemical energy conversion. Non-ideal batteries will be dealt with in terms of an "internal resistance".

+ -

V+ -

OR

Devices

• Resistors:

Purpose is to limit current drawn in a circuit.» Resistance can be calculated from knowledge of the

geometry of the resistor AND the “resistivity” of the material out of which it is made.

» The effective resistance of series and parallel combinations of resistors will be calculated using the concepts of potential difference and current conservation (Kirchoff’s Laws).

• Resistance

Resistance is defined to be the ratio of the applied voltage to the current passing through. V

I IR

UNIT: OHM =

How resistance is calculated

• Resistance – property of an object– depends on resistivity of its material and its geometry

• Resistivity – property of all materials– measures how much current density j results from a

given electric field E in that material

– units are Ohm x m (m)

• Conductivity– sometimes used instead of resistivity– measures the same thing as

• Conductance– sometimes used instead of resistance– measures the same thing as R

Resistors

in SeriesThe Voltage “drops”:

Whenever devices are in SERIES, the current is the same through both !

This reduces the circuit to:

a

c

Reffective

a

b

c

R1

R2

I

Hence:

Another (intuitive) way...

Consider two cylindrical resistors with lengths L1 and L2

V

R1

R2

L2

L1

Put them together, end to end to make a longer one...

Resistors in Parallel • What to do?

• But current through R1 is not I ! Call it I1. Similarly, R2 I2.

• How is I related to I 1 & I 2 ?? Current is conserved!

a

d

a

d

I

I

I

I

R1 R2

I1 I2

R

V

V

• Very generally, devices in parallel have the same voltage drop

Another (intuitive) way...

Consider two cylindrical resistors with cross-sectional areas A1 and A2

Put them together, side by side … to make a “fatter” one with A=A1+A2 ,

V R1

R2

A1A2

V R1

R2

V

R1

R2

Summary

• Resistors in series– the current is the same in

both R1 and R2

– the voltage drops add

• Resistors in parallel– the voltage drop is the same

in both R1 and R2

– the currents add