DC Circuits

P10-

Examples of Circuits

P10- 2

Current: Flow Of Charge

av Q

t

IAverage current Iav: Charge Q flowing across area A in time t

Instantaneous current: differential limit of Iav

P10- 3

I dQ

dtUnits of Current: Coulombs/second = Ampere

Direction of The CurrentDirection of current is direction of flow of pos. charge

or, opposite direction of flow of negative charge

P10- 4

Clicker question 1

Current Density JJ: current/unit area

Iˆ points in direction of current

J I

Iˆ

A

�

I J nˆ dA J

dA

SS

��

P10- 6

Why Does Current Flow?If an electric field is set up in a conductor, charge will move (making a current in direction of E).

Negative charges will move opposite to E’s direction, The resulted current is still in the same direction as E.

Note that when current is flowing, the conductor is not an equipotential surface (and Einside ≠ 0)!

P10- 7

P10-10

Microscopic Picture

Drift speed is velocity forced by applied electric field in the presence of collisions.

It is typically 4x10-5 m/sec, or 0.04 mm/second!

To go one meter at this speed takes about 10 hours!

How Can This Be?

Conductivity and ResistivityAbility of current to flow depends on density of charges & rate of scattering

P10-9

Two quantities summarize this:

: conductivity

: resistivity

Microscopic Ohm’s Law

J E or E Jor

� � ��

1

P10-10

and depend only on the microscopic properties of the material, not on its shape

If current density j is uniform and perpendicular to the cross-section area, I=jA

Temperature Effects on

P10-11

For metals, the resistivity is extremely low, because there are a lot of free charges. The resistivity linearly increases with increasing temperature over a large range of T: Because at higher T, the free charges will be blocked more by the active lattices of atoms.

Semiconductors, such as silicon, have little free charges. When temperature increases, more electrons can be set free, hence the conductivity increases and resistivity decreases.

PRS Questions: Resistance?

P10-12

Why Does Current Flow?Instead of thinking of Electric Field, think of potential difference across the conductor

P10-13

Ohm’s Law

V IR

P10-15

R kL

AR has units of Ohms () = Volts/Amp

I=DV/R; Current is determined by the potential difference DV and the resistance R between any two points. R= DV/I; The electrical resistance of a circuit component is the potential difference DV between its ends divided by the current I, that is established in response to the potential difference.

Electrical Power

Power is change in energy per unit time

So power to move current through circuit elements:

P d U d qV dq V dtdt dt

P10-16

P I V

Power - Battery

Moving from the negative to positive terminal of a battery increases your potential. If current flows in that direction the battery supplies power

I

P10-17

Psupplied I V I

Power - ResistorMoving across a resistor in the direction of current decreases your potential.

Resistors always dissipate power whenever there is current and convert electrical potential energy into heat.

This is also called Ohmic losses or Joule heating.

P10-18

When the potential drop across the resistor, DV, is fixed, the rate of Joule heating is reversely proportional to R.

When the current through the resistor, I, is fixed, the rate of Joule heating is proportional to R.

Please notice that regular metal wires has very little resistance comparing to the actual resistors we use in a circuit. In general, we consider there is no resistance and voltage drop in wires, even when a current flows.

Power - Resistor

PRS Questions: More Light Bulbs

P10-41

Symbols for Circuit Elements

P10-21

Battery

Resistor

Capacitor

Switch

Sign Conventions - Battery

Moving from the negative to positive terminal of a battery increases your potential

V Vb Va

Think:

Ski Lift

P10-22

Sign Conventions - Resistor

Moving across a resistor in the direction of currentdecreases your potential

V Vb Va

Think:

Ski Slope

P10-23

Sign Conventions - Capacitor

Moving across a capacitor from the negatively to positively charged plate increases your potential

V Vb Va

Think:

Ski Lodge

P10-24

Series vs. Parallel

Series

P10-25

Parallel

Resistors In SeriesThe same current I must flow through both resistors

V I R1 I R2 I (R1 R2 ) I Req

R1 R2Req

P10-26

Resistors In ParallelVoltage drop across the resistors must be the same

V V1 V2 I1R1 I2 R2 IReq

R1 R2

1 1 1 Req

I I1 I2

P10-27

V V VR1 R2

Req

PRS Questions: More Light Bulbs

P10-41