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PHY-2049. Current & Circuits February ‘08. A closed circuit. Hot, Hot Hot. Power in DC Circuit. copper. 12 volts 0 volts.

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phy 2049

PHY-2049

Current & Circuits

February ‘08

a closed circuit
A closed circuit

Hot, Hot Hot

slide4

copper

12 volts 0 volts

The figure below gives the electrical potential V(x) along a copper wire carrying a uniform current, from a point at higher potential (x=0m) to a point at a lower potential (x=3m). The wire has a radius of 2.45 mm. What is the current in the wire?

What does the graph tell us??

*The length of the wire is 3 meters.

*The potential difference across the

wire is 12 m volts.

*The wire is uniform.

Let’s get rid of the mm radius and

convert it to area in square meters:

A=pr2 = 3.14159 x 2.452 x 10-6 m2

or

A=1.9 x 10-5 m 2

Material is Copper so resistivity is (from table) = 1.69 x 10-8 ohm meters

series combinations

R1 R2

V1 V2

V

i

i

Series Combinations

SERIES Resistors

slide8

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?

what s this
What’s This???

In Fig. 28-39, find the equivalent resistance between points (a) F and H and [2.5](b) F and G. [3.13]

?

slide11
(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
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 source is not an ideal battery

V

By the way …. this is called a circuit!

A REAL Power Sourceis NOT an ideal battery

Internal Resistance

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

a physical real battery
A Physical (Real) Battery

Internal Resistance

back to potential

Represents a charge in space

Back to Potential

Change in potential as one circuits

this complete circuit is ZERO!

consider a circuit
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
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.
new laws passed by this session of the floriduh legislature
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
a single real resistor can be modeled as follows
A single “real” resistor can be modeledas follows:

R

b

a

V

position

ADD ENOUGH RESISTORS, MAKING THEM SMALLER

AND 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
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.
multiple batteries
Multiple Batteries

Watch the DIRECTION !!

reduction
Reduction

Computes i

the unthinkable
The Unthinkable ….

Resistors and Capacitors in the same circuit??

Is this cruel or what??

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.

RC Circuit

How Fast ?

close the switch

What do you

think will

happen when

we close the

swutch?

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
Really Close the Switch

I need to use E for E

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

= Coul/(Coul/sec) = (1/sec)

this is a differential equation
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!
discharging a capacitor
Discharging a Capacitor

qinitial=CE BIG SURPRISE! (Q=CV)

i

iR+q/C=0

slide40

In Fig. (a), a R = 21, Ohma resistor is connected to a battery. Figure (b) shows the increase

  • of thermal energy Eth in the resistor as a function of time t.
  • What is the electric potential across the battery? (60)
  • If the resistance is doubled, what is the POWER dissipated by the circuit? (39)
  • Did you put your name on your paper? (1)

Looking at the graph, we see that the

resistor dissipates 0.5 mJ in one second.

Therefore, the POWER =i2R=0.5 mW