PHY-2049 Current & Circuits February ‘08. News Quiz Today Examination #2 is on Wednesday of...

PHY-2049Current & CircuitsFebruary ‘08

News•Quiz Today•Examination #2 is on Wednesday of next

week (2/4/09)• It covers potential, capacitors, resistors and

any material covered through Monday on DC circuits.

•No review session on Wednesday – Exam Day!

A closed circuit

Hot, H

ot H

ot

Power in DC Circuit

R

EIVRIP

RIIRIIVPPower

VIt

QV

t

22

2

W

:Power

QVW

:isbattery by the done

workofamount The battery. by theresistor the

throughpushed is Q charge a t, In time

Let’s add resistors …….

Series Combinations

iiRseriesR

general

RRR

iRiRiRVVV

and

iRV

iRV

)(

:21

2121

22

11

R1 R2

i i

V1 V2V

SERIES Resistors

The rod in the figure is made of two materials. The figure is not drawn to scale. Each conductor has a square cross section 3.00 mm on a side. The first material has a resistivity of 4.00 × 10–3 Ω · m and is 25.0 cm long, while the second material has a resistivity of 6.00 × 10–3 Ω · m and is 40.0 cm long. What is the resistance between the ends of the rod?

Parallel Combination??

i iRR

general

RRR

so

R

V

R

V

R

Viii

iRV

11

111

..

21

2121

R1, I1

R2, I2

V

What’s This???

In the figure, find the equivalent resistance between points (a) F and H and [2.5]  (b) F and G. [3.13]  

• (a) Find the equivalent resistance between points a and b in Figure P28.6. (b) A potential difference of 34.0 V is applied between points a and b. Calculate the current in each resistor.

Power Source in a Circuit

The ideal battery does work on charges moving them (inside) from a lower potential to one that is V higher.

A REAL Power Sourceis NOT an ideal battery

V

E or Emf is an idealized device that does an amount of work E to move a unit charge from one side to another.

By the way …. this is called a circuit!

Internal Resistance

A Physical (Real) Battery

Rr

Emfi

Internal Resistance

Which is brighter?

Which is Brighter

Which is Brighter???

Back to Potential

Represents a charge in space

Change in potential as one circuitsthis complete circuit is ZERO!

Consider a “circuit”.

This trip around the circuit is the same as a path through space.

THE CHANGE IN POTENTIAL FROM “a” AROUND THE CIRCUIT AND BACK TO “a” is ZERO!!

To remember• In a real circuit, we can neglect the resistance

of the wires compared to the resistors.▫ We can therefore consider a wire in a circuit to be an

equipotential – the change in potential over its length is slight compared to that in a resistor

• A resistor allows current to flow from a high potential to a lower potential.

• The energy needed to do this is supplied by the battery.

VqW

NEW LAWS PASSED BY THIS SESSION OF THE FLORIDUH LEGISLATURE.

•LOOP EQUATION▫The sum of the voltage drops (or rises) as

one completely travels through a circuit loop is zero.

▫Sometimes known as Kirchoff’s loop equation.

•NODE EQUATION▫The sum of the currents entering (or

leaving) a node in a circuit is ZERO

TWO resistors again

jj

21

21

RR

Resistors SERIESfor General

RRR

or

iRiRiRV

i

R1 R2

V1 V2

V

A single “real” resistor can be modeledas follows:

R

a b

V

position

ADD ENOUGH RESISTORS, MAKING THEM SMALLERAND YOU MODEL A CONTINUOUS VOLTAGE DROP.

We start at a point in the circuit and travel around until we get back to where we started.

•If the potential rises … well it is a rise.•If it falls it is a fall OR a negative rise.•We can traverse the circuit adding each

rise or drop in potential.•The sum of all the rises around the loop is

zero. A drop is a negative rise.•The sum of all the drops around a circuit

is zero. A rise is a negative drop.•Your choice … rises or drops. But you

must remain consistent.

Take a trip around this circuit.

Consider voltage DROPS:

-E +ir +iR = 0or

E=ir + iRrise

Circuit Reduction

i=E/Req

Reduction

Computes i

Another Reduction Example

PARALLEL

1212

1

600

50

30

1

20

11

RR

Battery

•A battery applies a potential difference between its terminals.

•Whatever else is connected (circuits, etc.), the potential between the points remains the same: the battery potential.

Take a trip around this circuit.

Consider voltage DROPS:

-E +ir +iR = 0or

E=ir + iRrise

Multiple Batteries

START by assuming a DIRECTION for each Current

Let’s write the equations.

In the figure, all the resistors have a resistance of 4.0 and all the (ideal) batteries have an emf of 4.0 V. What is the current through resistor R?

Consider the circuit shown in the figure. Find (a) the current in the 20.0-Ω resistor and (b) the potential difference between points a and b.

Using Kirchhoff’s rules, (a) find the current in each resistor in Figure P28.24. (b) Find the potential difference between points c and f. Which point is at thehigher potential?

The Unthinkable ….

RC Circuit• Initially, no current

through the circuit• Close switch at (a) and

current begins to flow until the capacitor is fully charged.

• If capacitor is charged and switch is switched to (b) discharge will follow.

Close the Switch

I need to use E for E

Note RC = (Volts/Amp)(Coul/Volt) = Coul/(Coul/sec) = (1/sec)

Really Close the Switch

I need to use E for E

R

E

RC

q

dt

dq

or

EC

q

dt

dqR

C

qiRE

dt

dqi since

0

Equation Loop

Note RC = (Volts/Amp)(Coul/Volt) = Coul/(Coul/sec) = (1/sec)

This is a differential equation.

•To solve we need what is called a particular solution as well as a general solution.

•We often do this by creative “guessing” and then matching the guess to reality.

•You may or may not have studied this topic … but you WILL!

RC

REaeCE

R

E

RC

q

dt

dq

CEq

R

E

RC

q

dt

dq

Keqq

at

p

atp

1

RCE

Ea

E/R0CEa

0for t

/)e-CE(1)(

)e-CE(1q and

-CEK

KCE0

solution from and 0q 0,When t

and 0dq/dt charged,fully is device When the

:solution particularat Look

Solution General

at-

at-

Time Constant

RC

Result q=CE(1-e-t/RC)

q=CE(1-e-t/RC) and i=(CE/RC) e-t/RC

RCteR

Ei /

Discharging a Capacitorqinitial=CE BIG SURPRISE! (Q=CV)

i

iR+q/C=0

RCt

RCt

eRC

q

dt

dqi

eqq

solutionC

q

dt

dqR

/0

/0

0