Lecture 3: Electric Current, Resistance, and Circuits

Electric current is the flow of electric charge.
It is defined as the amount of charge passing a given point per unit time.
I = \frac{\Delta Q}{\Delta t}, where:
- I is the electric current.
- \Delta Q is the amount of charge.
- \Delta t is the time interval.
The unit of electric current is the ampere (A), where 1 A = 1 Coulomb/second.
Example: A 1.5-volt AA battery rated for 3000 milliamp-hours (mAh) will transfer \Delta Q = I \times \Delta t = 3000 \times 10^{-3} \text{ A} \times 3600 \text{ s} = 1.1 \times 10^4 Coulombs of charge before it dies.
Batteries produce charge through chemical reactions and cannot be treated like capacitors.

In a conductor, electron shells overlap, allowing electrons to move freely.
Quantum mechanics reveals that electrons have wave-like properties, enabling them to travel along the atoms in a conductor like a traveling wave.
For proper electron flow, atoms need to be in the correct positions.
Disorder in the atomic structure decreases electron current because out-of-place atoms reflect electron waves backwards, causing a superposition of reflected waves that diminishes the net electron current.

Resistance hinders the flow of electrons.
It arises in pure materials due to temperature, which causes atoms to vibrate around their equilibrium positions.
Impurities in the material exacerbate resistance.
The symbol for resistance is a zigzag line, representing the uneven flow of electrons.
All conducting materials (except superconductors) have resistance.

Resistivity ($\rho$) is a material's intrinsic property that determines its resistance.
Resistance (R) is related to resistivity, length (L), and cross-sectional area (A) by the formula: R = \rho \frac{L}{A}.
Fat wires have low resistance, while long wires have high resistance.
In circuit analysis, wires are often treated as perfect conductors, and all resistance is concentrated in resistors.

As electrons collide with atoms in a resistor, they lose energy, which is converted into heat.
This energy loss per second is power (P), measured in watts.
The equations for power are:
- P = I^2R
- P = IV
- P = \frac{V^2}{R}
The appropriate equation to use depends on what is being held constant (current or voltage).

Electrons do not push each other through a wire; they move due to an electric potential difference (voltage), analogous to peas rolling downhill on a tilted knife.
Current in a circuit works like a conveyor belt; if the circuit is broken at any point, the current stops, because a continuous loop is necessary.
Electrons cannot be "squirted" out of a wire; a continuous circuit is required for current flow.

For calculations, current is treated as a flow of positive charges, even though it is actually electrons moving.
This convention simplifies calculations by avoiding the need for numerous negative signs.

In a circuit with a nine-volt battery, voltage differs only across components with resistance. There is no voltage drop across ideal wires.

When resistors are connected in series, the total voltage drop across the series is the sum of the individual voltage drops: V{AC} = V{AB} + V_{BC}.
The current is the same throughout a series circuit because charges have no other place to go.

When resistors are connected in parallel, the voltage across each resistor is the same.
The total current is the sum of the currents through each resistor.
Not every circuit is either purely series or purely parallel; some circuits have both types of elements.

Complex circuits can be analyzed by breaking them down into simpler series and parallel combinations.

For identical resistors and batteries, a parallel circuit will draw more current from the battery than a series circuit because it provides multiple paths for current flow.

Fuses protect circuits and devices from excessive current.
They are connected in series with the device they protect to ensure they carry the same current.
Excessive current heats the fuse to its melting point, breaking the circuit.
Fuses are made of alloys with low melting points.
The fuse with the largest cross-sectional area (A) will have the lowest resistance (R), allowing a larger current (I) to flow before it melts, since P = I^2R and R = \rho \frac{L}{A}. A larger area gives the smallest resistance, therefore allowing a larger current to flow before melting the fuse, which is why big fat fuses are more desireable.