Capacitor Examples C 2C C C/2 d/4 3d/4 a

Current = charges in motion Electric Current Current = charges in motion Magnitude rate at which net positive charges move across a cross sectional surface Units: [I] = C/s = A (ampere) J = current density (vector) in A/m² Current is a scalar, signed quantity, whose sign corresponds to the direction of motion of net positive charges by convention

Microscopic View of Electric Current in Conductor A All charges move with some velocity ve random motion with high speeds (O(106)m/s) but with a drift in a certain direction on average if E is present thermal energy scattering off each other, defects, ions, … Give the value of the Vd from textbook. Drift velocity vd is orders of magnitudes less than the actual velocity of charges,

Current and Drift Velocity in Conductor Drift velocity vd is orders of magnitudes less than the actual velocity of charges.  where n =carrier density Vd~0.1mm/s In the following condition: I = 1.0A, copper: n ~1029atoms/m3 1mm radius wire. Vd~0.01mm/s

Ohm’s Law Current-Potential (I-V) characteristic of a device may or may not obey Ohm’s Law: or V  IR with R constant Resistance (ohms) gas in fluorescent tube tungsten wire diode

Resistance and Resitivity for Ohmic Material resistivity R (in ) resistance L A J is proportional to Vd which is proportional to acceleration which is proportional to E

Resistance V R I Resistance (definition) constant R Ohm’s Law

b) 1.6 mA c) 3.2 A d) 1.6A e) 3.2 mA Warm up There are 2x1014 electrons across a resistor in 10 seconds. What is the current through the resistor? a) 3.2mA b) 1.6 mA c) 3.2 A d) 1.6A e) 3.2 mA Note: e = 1.6x10-19 C V R I

Temperature Dependence of Resistivity Usually T0 is 293K (room temp.) Usually  > 0 (ρ increases as T ) Material 0 (m)  (K-1) Ag 1.6x10-8 3.8x10-3 Cu 1.7x10-8 3.9x10-3 Si 6.4x102 -7.5x10-2 glass 1010 ~ 1014 sulfur 1015 Copper Demo: measure R of electron bulb when T is high and low. Superconductivity at very low temperature

Electric Current and Joule Heating Free electrons in a conductor gains kinetic energy due to an externally applied E. Scattering from the atomic ions of the metal and other electrons quickly leads to a steady state with a constant current I. Transfers energy to the atoms of the solid (to vibrate), i.e., Joule heating. Hit an object with a hammer, the object become hot.

Energy in Electric Circuits Steady current means a constant amount of charge Q flows past any given cross section during time t, where I= Q / t. I I a b a b ∆Q ∆Q Energy lost by Q is => heat Read 27-8 (semi-conductor) and 27-9 (superconductor) So, Power dissipation = rate of decrease of U =

EMF – Electromotive Force An EMF device is a charge pump that can maintain a potential difference across two terminals by doing work on the charges when necessary. Examples: battery, fuel cell, electric generator, solar cell, fuel cell, thermopile, … Converts energy (chemical, mechanical, solar, thermal, …) into electrical energy. Within the EMF device, positive charges are lifted from lower to higher potential. If work dW is required to lift charge dq, EMF

Internal Resistance of a Battery load terminal voltage internal resistance

Energy Conservation A circuit consists of an ideal battery (B) with emf , a resistor R, and two connecting wires of negligible resistance. Energy conservation Work done by battery is equal to energy dissipated in resistor Ideal battery: no internal energy dissipation Real battery: internal energy dissipation exists dW > i2Rdt or  > iR=V

b) 1.0 Ω c) 2.5 Ω d) 3.0 Ω e) 4.0 Ω Lecture quiz A There are1014 electrons across a resistor with potential drop of 3.2mV in 10 seconds. What is the resistance of the resistor? a) 2.0 Ω b) 1.0 Ω c) 2.5 Ω d) 3.0 Ω e) 4.0 Ω Note: e = 1.6x10-19 C V R I

b)8.0 V c)2.5 V d)1.6 mV e)1.6mV Lecture quiz B There are 1014 electrons across a resistor of resistance 1.0Ω in 10 seconds. What is the potential drop across the resistor? a)3.2 mV b)8.0 V c)2.5 V d)1.6 mV e)1.6mV Note: e = 1.6x10-19 C V R I

b)8.0×1015 c)2.5×1012 d)4.0x1014 e)1.6×1019 Lecture quiz C The potential drop is 6.4mV across a resistor of resistance 1.0Ω. How many electrons enter the wire in 10 seconds? a)3.2×1019 b)8.0×1015 c)2.5×1012 d)4.0x1014 e)1.6×1019 Note: e = 1.6x10-19 C V R I