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 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

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

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

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

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

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

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

Resistivity

Why? The materials have different internal structures

and thus resist the flow of current differently They have different resistivities (symbol )

Resistivity is a property of a particular type of material rather than of a particular wire

Resistance

Short, wide wires have less resistance than long, narrow wires

The resistance can be written as: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)

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

Temperature Dependence

We use the relationship:

– 0 = 0(T – T0) Where:

0 is the resistivity at some reference temperature T0

is the temperature coefficient of resistivity

We look up 0 and in tables

Temperature Versus Resistance for a Metal

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

Semiconductors and Temperature

Superconductivity

The wire’s resistance slows down the electrons

Like a frictionless surface

Such materials are called superconductors Resistance generally decreases with decreasing T

Next Time

Read 26.4-26.9 Problems: Ch 26, P: 9, 22, 26, 36, 40

Consider a spherical capacitor. Which of the following would increase the capacitance the most (assuming no other changes)?

A) Doubling the radius of the inner sphereB) Doubling the radius of the outer sphereC) Doubling the radius of both inner and outer

spheresD) a and b tieE) None of the these changes would increase C

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?

A) Replace the air with vacuum

B) Replace the air with a copper plate

C) Replace the air with cardboard

D) Increase the separation of the plates

E) Use round plates instead of square ones

If the voltage across a capacitor is doubled, the amount of energy stored on the capacitor,

A) Is halvedB) Stays the sameC) Is doubledD) Is tripledE) Is quadrupled