Chapter 7: Parallel Circuits

 

Characteristics of a Parallel Circuit

In a parallel circuit, components are connected between the same two nodes, providing multiple paths for current flow. The same voltage appears across all parallel branches, but the current divides among them.

Key properties: (1) Voltage is the same across all parallel branches: V_T = V₁ = V₂ = V₃ = ... (2) Total current equals the sum of branch currents: I_T = I₁ + I₂ + I₃ + ... (3) Total resistance is less than the smallest individual resistance: 1/R_T = 1/R₁ + 1/R₂ + 1/R₃ + ...

 

Calculating Parallel Resistance

For two resistors in parallel, the formula simplifies to: R_T = (R₁ × R₂) / (R₁ + R₂). This is often called the 'product over sum' formula.

Example: A 100 Ω and 300 Ω resistor in parallel: R_T = (100 × 300) / (100 + 300) = 30000 / 400 = 75 Ω

Notice that 75 Ω is indeed less than the smaller resistor (100 Ω). Adding any resistance in parallel always decreases total resistance and increases total current draw from the source.

 

Current Divider Principle

Just as series circuits divide voltage, parallel circuits divide current. The current divider formula for two parallel resistors is: I₁ = I_T × (R₂ / (R₁ + R₂)). Note that the resistor in the denominator is the other resistor, not R₁. Larger resistance attracts less current — this is the key insight of the current divider.

Parallel circuits are the standard configuration for household electrical wiring. All appliances plug into sockets wired in parallel, ensuring each device receives the full mains voltage regardless of how many other devices are connected.