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Series & Parallel Circuits

Series Circuits

In a series circuit, components are connected end-to-end in a single path

Key Characteristics:

  • Same current flows through all components: $$I_{total} = I_1 = I_2 = I_3$$
  • Voltage divides across components: $$V_{total} = V_1 + V_2 + V_3$$
  • Resistances add up: $$R_{total} = R_1 + R_2 + R_3$$

Example: Two resistors in series

Battery: 9V, R1: 470Ω, R2: 330Ω

$$R_{total} = 470Ω + 330Ω = 800Ω$$

$$I = V / R_{total} = 9V / 800Ω = 11.25mA$$

$$V_1 = I × R_1 = 11.25mA × 470Ω = 5.29V$$

$$V_2 = I × R_2 = 11.25mA × 330Ω = 3.71V$$

5.29V + 3.71V = 9V ✓ (Kirchhoff's Voltage Law!)

Parallel Circuits

In a parallel circuit, components are connected across the same two points

Key Characteristics:

  • Same voltage across all components: $$V_{total} = V_1 = V_2 = V_3$$
  • Current divides among branches: $$I_{total} = I_1 + I_2 + I_3$$
  • Reciprocal resistances: $$1/R_{total} = 1/R_1 + 1/R_2 + 1/R_3$$

Example: Two resistors in parallel

Battery: 5V, R1: 220Ω, R2: 330Ω

$$1/R_{total} = 1/220Ω + 1/330Ω = 0.00758$$

$$R_{total} = 1/0.00758 = 132Ω$$

$$I_{total} = 5V / 132Ω = 37.9mA$$

$$I_1 = 5V / 220Ω = 22.7mA$$

$$I_2 = 5V / 330Ω = 15.2mA$$

22.7mA + 15.2mA = 37.9mA ✓ (Kirchhoff's Current Law!)

When to Use Series vs Parallel

Use Series When:

  • You want to limit current to all components equally (LED strings)
  • You need to divide voltage (voltage dividers)
  • You want components to turn on/off together (Christmas lights)
  • You need to add battery voltages (series batteries: 1.5V + 1.5V = 3V)

Use Parallel When:

  • You want each component to operate independently
  • You need the same voltage across all components (household outlets)
  • You want to increase current capacity (parallel batteries)
  • One component failing shouldn't affect others
Power in Series vs Parallel

Series Circuits:

$$P_{total} = P_1 + P_2 + P_3$$

Each component dissipates power based on its resistance

Parallel Circuits:

$$P_{total} = P_1 + P_2 + P_3$$

Total power is still the sum, but each component gets full voltage

In both cases, total power equals the sum of individual component powers. Energy is conserved!

Common Mistakes to Avoid
  • Assuming series resistances divide voltage equally - They don't! Voltage divides proportionally to resistance.
  • Thinking parallel resistances add - They don't! Use the reciprocal formula.
  • Forgetting total parallel resistance is always less than smallest resistor - Adding parallel paths reduces total resistance!
  • Mixing up which law applies - KVL for series loops, KCL for parallel junctions.

Practice in the Simulator!

Build these circuits to see the concepts in action:

  • Two LEDs in series with one resistor - notice they share current
  • Two LEDs in parallel with separate resistors - each operates independently
  • A voltage divider with two resistors to reduce voltage
  • Multiple batteries in series to add voltages
Start Building Circuits