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Current

Current. PH 203 Professor Lee Carkner Lecture 10. Circuit Theory. We have already discussed potential difference This charge motion is called the current (symbol: i) Energy can be extracted from the current due to resistance (symbol: R). Current. i = dq/dt

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Current

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  1. Current PH 203 Professor Lee Carkner Lecture 10

  2. Circuit Theory • We have already discussed potential difference • This charge motion is called the current (symbol: i) • Energy can be extracted from the current due to resistance (symbol: R)

  3. Current i = dq/dt • The units are amperes (amps) or coulombs per second • The most common charge carrier is the electron, but, • We draw the current as the direction positive particles would travel in

  4. Charge Conservation • If a current comes to a junction and splits into two currents, those two must sum up to equal the original i0 = i1 + i2 • Note that a single wire with no junctions has the same current everywhere

  5. Junctions • A junction is where the current splits • It has to make a choice • Note that “bends” are not junctions • Things in parallel must have a junction at each end

  6. Inside a Wire • What goes on inside a current carrying wire? • An applied potential difference makes them want to move in a certain direction (against the field) • They undergo many collisions and move in a random walk • Electrons do not move freely, directly or rapidly

  7. Current Density • Most wires can be thought of as cylinders with a particular radius and cross sectional area, A • We can combine the current and area to find the current density, J J = i/A • J is a vector in the same direction as the current

  8. Speed of Electrons • How fast are the charges moving? • What is q? • If n is the number of electrons per unit volume than the total charge is q= neLA • What is t? • vd = L/t • But t = q/i and q = neLA vd = Li/q = Li/neLA vd = i/neA

  9. Current Conundrums • The drift speed is very small (~mm per second), yet the effect of current is felt instantaneously • Electrons move randomly, yet current flows in only one direction • Between collisions they get back on track • Convention is based on the positive charge, but protons don’t normally move

  10. Resistivity • Why? • The materials have different internal structures and thus resist the flow of current differently • They have different resistivities (symbol r) • Resistivity is a property of a particular type of material rather than of a particular wire

  11. Resistance • Short, wide wires have less resistance than long, narrow wires • The resistance can be written as: R = r (L/A) • The units of resistance are ohms (volts per ampere) • Resistance tells how much current we will get for a given potential difference (R = V/i)

  12. Temperature and Resistance • Electronic devices get hot! • Temperature also affects electronic properties • This increased random motion means collisions are more frequent and it is harder for current to flow • Resistance generally increases with temperature

  13. Temperature Dependence • We use the relationship: r – r0 = r0a(T – T0) • Where: • r0 is the resistivity at some reference temperature T0 • a is the temperature coefficient of resistivity • We look up r0 and a in tables

  14. Temperature Versus Resistance for a Metal

  15. Semiconductors • Insulators have no free electrons • Conductors have many free electrons • Semiconductors are materials that have electrons that are moderately bound • Adding electrical or thermal energy can free the electrons and increase conductivity • At higher temperatures the larger thermal motions are offset by the greater availability of free electrons

  16. Semiconductors and Temperature

  17. Superconductivity • The wire’s resistance slows down the electrons • Like a frictionless surface • Such materials are called superconductors • Resistance generally decreases with decreasing T

  18. Next Time • Read 26.4-26.9 • Problems: Ch 26, P: 9, 22, 26, 36, 40

  19. Consider a spherical capacitor. Which of the following would increase the capacitance the most (assuming no other changes)? • Doubling the radius of the inner sphere • Doubling the radius of the outer sphere • Doubling the radius of both inner and outer spheres • a and b tie • None of the these changes would increase C

  20. Consider a pair of metal plates separated by an air gap that acts as a capacitor. How could the amount of charge on the plates be increased for a given voltage? • Replace the air with vacuum • Replace the air with a copper plate • Replace the air with cardboard • Increase the separation of the plates • Use round plates instead of square ones

  21. If the voltage across a capacitor is doubled, the amount of energy stored on the capacitor, • Is halved • Stays the same • Is doubled • Is tripled • Is quadrupled

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