Unit 10: Electric Circuits

1. Basic Circuit Concepts and Components

Electric circuits are pathways for electric charge to flow, creating useful electrical effects. Understanding the basic components and their relationships is crucial.

Key Components:
  • Resistors: Control current flow
  • Capacitors: Store electric charge
  • Batteries/Sources: Provide electrical potential difference
  • Conductors: Carry current with minimal resistance
V R

2. Ohm's Law and Resistance

Ohm's Law is the fundamental relationship between voltage, current, and resistance in electrical circuits.

V = IR
Where:
V = Voltage (Volts)
I = Current (Amperes)
R = Resistance (Ohms)
Temperature Effects: Resistance typically increases with temperature in metals according to:
R = R₀[1 + α(T - T₀)]
Example: A 12V battery is connected to a 6Ω resistor. Calculate the current:
I = V/R = 12V/6Ω = 2A

3. Series and Parallel Circuits

Understanding how components combine in series and parallel is essential for circuit analysis.

Series Resistors:
R_total = R₁ + R₂ + R₃ + ...

Parallel Resistors:
1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...
Series: Parallel:

4. Kirchhoff's Laws

Kirchhoff's Laws are fundamental principles for analyzing complex circuits:

Kirchhoff's Current Law (KCL): The sum of currents entering a node equals the sum of currents leaving it.
ΣI_in = ΣI_out
Kirchhoff's Voltage Law (KVL): The sum of voltage drops around any closed loop equals zero.
ΣV = 0
Example: Analyze a circuit with two loops and three resistors using KVL and KCL.

5. Capacitors in DC Circuits

Capacitors store electric charge and energy in electric fields.

C = Q/V
Energy stored: U = ½CV²
Time constant: τ = RC
Charging/Discharging:
V(t) = V₀(1 - e^(-t/RC)) [charging]
V(t) = V₀e^(-t/RC) [discharging]

6. Power and Energy in Circuits

Understanding power and energy consumption in circuits is crucial for practical applications.

Power:
P = VI = I²R = V²/R

Energy:
E = Pt
Example: Calculate the power dissipated in a 100Ω resistor with 2A current:
P = I²R = (2A)²(100Ω) = 400W

7. Complex Circuit Analysis

Methods for analyzing complex circuits with multiple components and loops.

Analysis Methods:
  • Mesh Analysis
  • Nodal Analysis
  • Thévenin's Theorem
  • Norton's Theorem
Thévenin's Theorem:
V_th = V_open circuit
R_th = R_equivalent with sources zeroed

8. RC Circuits: Transient Analysis

Understanding how circuits behave during transitions between states.

Current in RC circuit:
I(t) = (V₀/R)e^(-t/RC) [discharging]
I(t) = (V₀/R)(1 - e^(-t/RC)) [charging]
V t

9. Practical Applications and Measurements

Understanding how to measure circuit parameters and common applications.

Measuring Instruments:
  • Voltmeter: Connected in parallel
  • Ammeter: Connected in series
  • Ohmmeter: Circuit must be unpowered
  • Oscilloscope: Visualize time-varying signals
Application: Design a voltage divider circuit to convert 12V to 5V output.

10. Laboratory Safety and Best Practices

Essential safety considerations when working with electrical circuits.

Safety Guidelines:
  • Always double-check connections before powering on
  • Use appropriate current and voltage ratings
  • Keep workspace dry and clean
  • Use proper grounding techniques
  • Have emergency shutdown procedures ready