DC Circuits P10-

Examples of Circuits P10-

Current: Flow Of Charge  Q t Average current Iav: Charge Q flowing across area A in time t I av Instantaneous current: differential limit of Iav I  dQ dt Units of Current: Coulombs/second = Ampere P10-

Direction of The Current Direction of current is direction of flow of pos. charge or, opposite direction of flow of negative charge P10-

Clicker question 1

J  I Iˆ Iˆ points in direction of current � � Current Density J J: current/unit area � J  I Iˆ A Iˆ points in direction of current � � I   J  nˆ dA  J  dA S S P10-

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-

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? P10-10

Conductivity and Resistivity Ability of current to flow depends on density of charges & rate of scattering Two quantities summarize this: : conductivity : resistivity

  1 � � � � J   E or E  J or  Microscopic Ohm’s Law � � � � J   E or E  J or   1   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  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?

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

Ohm’s Law V IR 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. R  kL A R has units of Ohms () = Volts/Amp

P  I V Electrical Power P  d U  d qV   dq V dt dt dt Power is change in energy per unit time So power to move current through circuit elements: P  d U  d qV   dq V dt dt dt P  I V

Power - Battery Psupplied  I V  I  Moving from the negative to positive terminal of a battery increases your potential. If current flows in that direction the battery supplies power I Psupplied  I V  I 

Power - Resistor Moving 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.

Power - Resistor 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.

PRS Questions: More Light Bulbs

Symbols for Circuit Elements 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

Sign Conventions - Resistor Moving across a resistor in the direction of current decreases your potential V  Vb Va Think: Ski Slope

Sign Conventions - Capacitor Moving across a capacitor from the negatively to positively charged plate increases your potential V  Vb Va Think: Ski Lodge

Series vs. Parallel Series Parallel

Req V  I R1  I R2  I (R1  R2 )  I Req  R1  R2 Resistors In Series The same current I must flow through both resistors V  I R1  I R2  I (R1  R2 )  I Req Req  R1  R2

Req Resistors In Parallel R1 R2 Req 1  1  1 R1 R2 Voltage drop across the resistors must be the same V  V1  V2  I1R1  I2 R2  IReq V V V R1 R2 Req 1  1  1 I  I1  I2    Req R1 R2

PRS Questions: More Light Bulbs