Lecture 17 - Voltage, Current, Resistance, and Power

Lecture 17 focused on key concepts related to voltage, current, resistance, and power in electrical circuits.

Definition: Electric potential; can be thought of as the "push" that drives current through a circuit.
Also referred to as Electromotive Force (EMF); specifically, the voltage of a battery, signifying its source.
Measured in Volts (V).

Definition: The flow of electric charge; it flows from the positive (high potential) to the negative terminal (lower potential).
Measured in Amperes (A); units for current are Coulombs per second (C/s).
Current equation: $i = rac{q}{ riangle t}$ where ( q ) is charge in Coulombs and ( \triangle t ) is time in seconds.

Definition: The opposition that a material offers to the flow of electric current, resulting in a specific voltage drop across it.
Measured in Ohms (Ω).
Ohm's Law: $V = iR$ , relates voltage (V), current (i), and resistance (R).
Factors affecting resistance:
- Directly proportional to the length of the conductor (increased length increases resistance).
- Inversely proportional to the cross-sectional area of the conductor (increased area decreases resistance).
- Dependent on the material's inherent resistivity (( \rho )).
- Resistance formula: $R = \frac{\rho L}{A}$ , where ( L ) is the length and ( A ) is the cross-sectional area.

Definition: The rate at which electric energy is consumed or converted to another form of energy (like heat, light, etc.).
Measured in Watts (W); 1 Watt = 1 Joule/second (J/s).
Power formulas include:
- $P = iV$ (using voltage and current),
- $P = \frac{V^2}{R}$ (using voltage and resistance),
- $P = i^2R$ (using current and resistance).

Relation to Power: $E = Pt$ , where:
- ( P ) is power,
- ( t ) is time in seconds.
Units of energy include Joules (J) and can also be expressed in kilowatt-hours (kWh).
Energy cost calculation for electrical use:
- Electricity typically costs around $0.10 per kWh.
- Example: If a device uses 200W for 1 hour, the cost is calculated as:
  $ext{Energy} = (0.2 ext{kW})(1 ext{hour}) = 0.2 ext{kWh}$
  $ext{Cost} = (0.2 ext{kWh}) imes ( ext{ extdollar}0.10/ ext{kWh}) = ext{ extdollar}0.02$

Definition: Circuit elements designed to provide specific resistance to the flow of current.
Symbol in circuit diagrams: R.
Types of resistors may include:
- Variable resistors (potentiometers),
- Standard resistors, electric bulbs as resistors (not strictly linear).

Function: Provide a fixed amount of EMF (electric potential) across a circuit with terminals at different potentials.
Series connections of batteries increase total EMF, where the total voltage $V = ext{sum of all individual EMFs}$
Common battery voltages:
- AA, AAA, C, D cells = 1.5V,
- 9V batteries = 9V,
- Car batteries = 12V.

Definition: Electric current that periodically reverses direction; in contrast to Direct Current (DC) where the flow is unidirectional.
AC voltage and current can be modeled as: $ext{EMF}(t) = ext{EMF}_0 imes ext{sin}(2\pi ft)$
- where ( f ) is the frequency of the AC source (typically 60 Hz in the USA).
Root-mean-square (rms) values are used for AC, defined as: $V_{rms} = \frac{\sqrt{\langle V^2 \rangle}}{\sqrt{n}}$
- Typical outlet voltage values: 120V (rms) in USA, 240V in Europe.

Importance of Current: Current, not voltage, can cause harm to the human body.
Safety thresholds:
- 0.001 A: sensation felt,
- >0.01 A: painful shock,
- 0.1-0.2 A: potentially fatal due to ventricular fibrillation,
- >0.2 A: serious burns and can lead to unconsciousness.

When evaluating circuits, the relationship between power, resistance, and current through Ohm's Law and power formulas aids in understanding energy use in devices.