Current and Resistance Current (I) is the rate a charge flows through a surface. The direction of flow is perpendicular to that surface area. Current is equal to the amount of charge per unit time. I =  Q/  t C/s or amperes (A) Charges flowing through a surface can be +ve, -ve or both. The direction of flow is by convention the direction of +ve flow.

Current cont. In a common conductor the current is due to the motion of -ve charged electrons, so the direction of the current is opposite to the motion of the electrons. In a particle accelerator the +ve protons are moving in the sane direction as the current. In gases and electrolytes the current is a result of both +ve and -ve particles.

Cont. A moving charge is called a charge carrier In electrostatics the charge is stationary and the electric potential is the same everywhere. For conductors carrying a current moving along a wire, the electric potential is continually decreasing, except for superconductors.

Current and Drift Speed Consider a conductor where the charge carriers are electrons. As the electrons move through the metal conductor they undergo random motion colliding with the metal atoms. The motion is a zig zag style which is much slower than the movement of fre electrons. (Drift Speed) The energy transferred from the electrons to the metal causes the temperature of the conductor to increase

Cont. Despite the collisions, electrons move slowly along the conductor in a direction opposite to the electric field (E) with a drift speed of v d. Let  Q = mobile charge in a conductor n = number of carriers, q = charge on carrier, A = area,  x = distance traveled, If Q = (nAv d  t)q and I =  Q/  t then I = nAv d q

Voltage Measurements in Circuits A circuit means a closed loop in which a current can flow. Consider, V - + Ammeter A Voltmeter Bulb Battery

Cont. The battery pumps charge through the bulb around the loop. The current (A) in the bulb is measured by the ammeter, all the current must pass through the ammeter before passing the bulb. The voltmeter measured the potential difference (V) between the two ends of the bulb’s filament.

Resistance and Ohm’s Law When a voltage is applied across a conductor the current that flows is proportional to that voltage. Resistance is a ratio of voltage to current. R =  V/I volts/ampere = Ohm (  ) Resistance in a circuit result from the collision of electrons with the atoms in a conductor. Resistance remains constant over a wide range of applied voltages or currents ( Ohm’s Law)

Cont. R is independent of V and I A resistor is a conductor that provides a specified resistance in a circuit. Materials that have a constant resistance are called ohmic. Those whose resistance changes with voltage and current are nonohmic.(Diode) Resistance is small for +ve V and large for-ve V

Resistivity The collision of electrons with a material atoms is the origin of a material’s resistance The resistance of a ohmic material increases with its length. A small cross-sectional area also increases resistance. R =  l/A where  = the material’s resistivity which is particular to the material and its temperature. A good conductor has low resistivity, in ohms per meter.

Temperature Variation of Resistance Resistance increases with increase in temperature.  =  o [1+  (T-T 0 )] where  o is the resistivity at T o (published reference level) As resistance is proportional to resistivity R = R o [1+  (T-T 0 )] where  is a parameter called the temperature coefficient of resistivity. ( particular to material)

Superconductors Superconductors are materials whose resistance falls to zero below a critical temperature T c. ( mercury below 4.1 K) T c is sensitive to chemical composition, pressure and crystalline structure. Al, Sn, Pb Once a current is set up in a superconductor it persists without any applied voltage as R = 0.

Superconductors cont. Copper oxides at 30 K, a yttrium/barium/copper oxide at 92K, Bismuth, strontium, calcium and copper oxides at 105K, mercury oxides at 150K Superconducting magnet with magnetic fields 10 times stronger than ordinary magnet use to store energy.

Electrical Energy and Power Consider the following circuit a b c d - + Ground R

Power cont. The +ve terminal has the higher potential follow a charge Q through the battery from a which is grounded and of zero potential to b. The potential energy of the system increased by  Q  V and the battery decreased by the same amount. Neglecting resistance in the connecting wires no loss occurs between b c and d a

Power cont. As the charge carrier moves from c to d internal friction in R causes a loss of potential energy of the charge and an increase of internal energy of the resistor (due to vibrations) in the form of heat. When the charge returns to a some of the chemical potential energy of the battery has been delivered to the resistor increasing its temperature.

Power cont. The charge  Q loses energy  Q  V as it passes through the resistor in time  t. The rate of loss is (  Q  V)/  t = I  V The rate at which the system losses potential energy is the same as the rate the resistor gains energy which is equal to power P = I  V in Watts as  V = IR then P = I 2 R =  V 2 /R