⚾️Honors Physics Unit 19 – Electrical Circuits

Key Concepts and Definitions

• Electric current ($I$) flow of electric charge through a conductor measured in amperes (A)
• Voltage ($V$) electric potential difference between two points in a circuit measured in volts (V)
  • Voltage sources provide the energy to move charges through a circuit (batteries, generators)
• Resistance ($R$) opposition to the flow of electric current measured in ohms ($\Omega$)
  • Conductors (copper wire) have low resistance allowing current to flow easily
  • Insulators (rubber, plastic) have high resistance preventing current flow
• Electric power ($P$) rate at which electrical energy is converted to other forms (heat, light) measured in watts (W)
• Conventional current assumes positive charges flow from positive to negative terminal
  • In reality, electrons flow from negative to positive terminal
• Direct current (DC) current flows in one direction only (batteries)
• Alternating current (AC) current periodically reverses direction (household outlets)

Circuit Components and Symbols

• Resistors ($R$) components that resist the flow of current represented by a zigzag line
  • Fixed resistors have a constant resistance value
  • Variable resistors (potentiometers) allow resistance to be adjusted
• Capacitors ($C$) components that store electric charge represented by two parallel lines
  • Act as temporary batteries releasing stored charge when voltage is removed
• Inductors ($L$) components that store energy in a magnetic field represented by a coiled wire
• Switches control the flow of current in a circuit represented by a line with a break
  • Open switch breaks the circuit preventing current flow
  • Closed switch completes the circuit allowing current flow
• Voltage sources (batteries, generators) provide energy to the circuit represented by two parallel lines one longer than the other
• Ammeters measure current connected in series with the circuit component
• Voltmeters measure voltage connected in parallel across the circuit component
• Ground reference point in a circuit represented by three descending lines

Types of Circuits

• Series circuits components connected end-to-end forming a single path for current
  • Current is the same through all components
  • Total resistance is the sum of individual resistances ($R_{total} = R_1 + R_2 + ...$)
  • Voltage divides across each component proportional to its resistance
• Parallel circuits components connected side-by-side forming multiple paths for current
  • Voltage is the same across all components
  • Total resistance is less than the smallest individual resistance ($\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$)
  • Current divides among the branches inversely proportional to their resistance
• Series-parallel circuits combination of series and parallel connections
  • Simplify by identifying and combining series and parallel sections
• Short circuits low resistance path causing excessive current potentially damaging components
• Open circuits break in the circuit path preventing current flow

Ohm's Law and Basic Calculations

• Ohm's Law relationship between voltage, current, and resistance in a circuit ($V = IR$)
  • Doubling voltage doubles current if resistance is constant
  • Doubling resistance halves current if voltage is constant
• Calculating resistance given voltage and current ($R = \frac{V}{I}$)
• Calculating current given voltage and resistance ($I = \frac{V}{R}$)
• Calculating voltage given current and resistance ($V = IR$)
• Power calculations
  • Power equals voltage times current ($P = VI$)
  • Power equals current squared times resistance ($P = I^2R$)
  • Power equals voltage squared divided by resistance ($P = \frac{V^2}{R}$)
• Energy calculations
  • Energy equals power times time ($E = Pt$) measured in joules (J)
  • Kilowatt-hour (kWh) common unit of electrical energy (1 kWh = 3.6 MJ)

Kirchhoff's Laws

• Kirchhoff's Current Law (KCL) sum of currents entering a node equals sum of currents leaving the node
  • Current is conserved at each junction in a circuit
  • Helps determine unknown currents in a circuit
• Kirchhoff's Voltage Law (KVL) sum of voltages around any closed loop in a circuit equals zero
  • Voltage rises and drops balance each other out
  • Helps determine unknown voltages in a circuit
• Steps for applying Kirchhoff's Laws
  1. Assign labels and directions for currents and voltages
  2. Apply KCL to each node to obtain current equations
  3. Apply KVL to each loop to obtain voltage equations
  4. Solve the system of equations for unknown quantities
• Kirchhoff's Laws are fundamental principles for analyzing complex circuits

Power in Electrical Circuits

• Electrical power rate at which electrical energy is converted to other forms (heat, light, mechanical)
• Power dissipation in resistors
  • Resistors convert electrical energy to heat ($P = I^2R$)
  • Power rating maximum power a resistor can safely dissipate without damage
• Power in voltage sources
  • Batteries and generators supply power to the circuit ($P = VI$)
  • Negative power indicates the source is providing power to the circuit
• Power in capacitors and inductors
  • Capacitors and inductors store energy in electric and magnetic fields
  • Average power over a complete cycle is zero (energy is stored and released)
• Efficiency ratio of useful output power to total input power ($\eta = \frac{P_{out}}{P_{in}}$)
  • Expressed as a percentage (100% = perfect efficiency)
  • Power loss due to heating in circuit components reduces efficiency

Measuring Electrical Quantities

• Ammeter measures electric current
  • Connected in series with the circuit component
  • Ideally has zero resistance to avoid affecting the circuit
• Voltmeter measures voltage
  • Connected in parallel across the circuit component
  • Ideally has infinite resistance to avoid drawing current from the circuit
• Ohmmeter measures resistance
  • Connected across the component with the circuit power off
  • Supplies a known current and measures the resulting voltage
• Multimeter combines ammeter, voltmeter, and ohmmeter in a single device
  • Allows measurement of current, voltage, and resistance
  • Some models also measure capacitance, inductance, and other quantities
• Oscilloscope displays voltage waveforms over time
  • Helps visualize and analyze AC signals and transient behavior
• Safety precautions when measuring electrical quantities
  • Ensure the meter is set to the correct mode and range
  • Start with the highest range and work down to avoid damage
  • Turn off power and discharge capacitors before connecting or disconnecting meters

Real-World Applications and Examples

• Household wiring
  • Outlets connected in parallel to maintain constant voltage (120 V in North America)
  • Switches and fuses connected in series to control and protect circuits
• Automotive electrical systems
  • 12 V battery supplies power to various loads (headlights, radio, engine control)
  • Fuses and circuit breakers protect against short circuits and overloads
• Electronic devices (smartphones, computers)
  • Complex circuits with many components (resistors, capacitors, inductors, transistors)
  • Integrated circuits (ICs) combine many components on a single chip
• Renewable energy systems
  • Solar panels generate DC voltage from sunlight
  • Inverters convert DC to AC for household use or grid connection
  • Batteries store excess energy for later use
• Electrical safety
  • Ground Fault Circuit Interrupters (GFCIs) protect against electric shock
  • Arc Fault Circuit Interrupters (AFCIs) protect against electrical fires
  • Proper grounding and insulation prevent dangerous voltages and currents