Series vs Parallel Circuits (with Real Multimeter Measurements)

In a **Series Circuit**, components are connected end-to-end in a single continuous chain. There is only **one path** for electrons to travel. ### Fundamental Series Rules: 1. **Current (I) is Constant**: Every electron passing through resistor R_1 must also pass through R_2 and R_3. **Formula:** I_total = I_1 = I_2 = I_3 2. **Equivalent Resistance (R_eq) Adds Up**: **Formula:** R_eq = R_1 + R_2 + R_3 3. **Voltage Divides (V)**: Total supply voltage equals the sum of voltage drops across individual components: **Formula:** V_total = V_1 + V_2 + V_3

### Circuit Components: - Supply Voltage: V_in = 9.00V - R_1 = 220 Ω, R_2 = 470 Ω, R_3 = 1000 Ω (1 kΩ) ### Calculations: **Formula:** R_eq = 220 + 470 + 1000 = 1690 Ω = 1.69 kΩ **Formula:** I = (V / R_eq) = (9.00 V / 1690 Ω) = 5.33mA ### Predicted Voltage Drops: - V_R1 = 5.33mA × 220 Ω = 1.17V - V_R2 = 5.33mA × 470 Ω = 2.50V - V_R3 = 5.33mA × 1000 Ω = 5.33V - Sum = 1.17 + 2.50 + 5.33 = 9.00V ### Multimeter Lab Verification: Take your digital multimeter in DC Volts mode and place probes across R_1, R_2, and R_3. Your real measurements will match calculations within resistor tolerance!

In a **Parallel Circuit**, all components are connected across the exact same two electrical nodes (power rails). ### Fundamental Parallel Rules: 1. **Voltage (V) is Constant**: Full supply voltage appears across every branch. **Formula:** V_total = V_1 = V_2 = V_3 2. **Current (I) Splits**: Total current is the sum of currents flowing through each branch. **Formula:** I_total = I_1 + I_2 + I_3 3. **Equivalent Resistance Formula**: **Formula:** (1 / R_eq) = (1 / R_1) + (1 / R_2) + (1 / R_3) *For 2 Resistors*: **Formula:** R_eq = (R_1 × R_2 / R_1 + R_2)

### Circuit Components: - V_in = 5.00V - R_1 = 100 Ω, R_2 = 220 Ω, R_3 = 470 Ω ### Calculations: **Formula:** (1 / R_eq) = (1 / 100) + (1 / 220) + (1 / 470) = 0.0100 + 0.00454 + 0.00213 = 0.01667 Ω^-1 **Formula:** R_eq = (1 / 0.01667) = 60.0 Ω ### Branch Currents: - I_1 = (5V / 100 Ω) = 50.0mA - I_2 = (5V / 220 Ω) = 22.7mA - I_3 = (5V / 470 Ω) = 10.6mA - I_total = 50.0 + 22.7 + 10.6 = 83.3mA

A notorious beginner error is wiring multiple LEDs in parallel with a single shared resistor to save board space. ### The Physics of LED Thermal Runaway: Because of semiconductor manufacturing variations, no two LEDs have identical forward voltages (V_f). 1. The LED with the slightly lower V_f (e.g. 1.98V vs 2.02V) conducts current first. 2. Drawing more current heats up the LED die. 3. As semiconductor temperature rises, forward voltage drops further (-≈ 2mV/^circC), causing it to hog even MORE current. 4. The hot LED burns out rapidly, dumping all current into the remaining LEDs, which burn out sequentially in a cascade! > [!WARNING] > **The Golden LED Rule**: Always give every individual LED its own dedicated series current-limiting resistor when connecting to a common power rail!