Wiring it Up: Series and Parallel Circuits
An electric circuit is a closed path through which an electric current can flow. Resistors (components that resist current flow) in a circuit can be connected in two basic ways: series or parallel.
Series Circuits
Configuration: Components are connected end-to-end, providing only one path for the current to flow.
Current: The current is the same through every component in the circuit. (I_total = I₁ = I₂ = ...).
Voltage: The total voltage from the source is divided among the components. The sum of the voltage drops across each resistor equals the total voltage. (V_total = V₁ + V₂ + ...).
Equivalent Resistance (Rₑₑ): The total resistance of the circuit is the sum of the individual resistances.
Rₑₑ = R₁ + R₂ + ...
Effect of Adding a Resistor: Adding another resistor in series increases the total resistance and decreases the total current. If one bulb in a string of old Christmas lights burns out (breaking the circuit), all the lights go out.
Parallel Circuits
Configuration: Components are connected across the same two points, providing multiple paths for the current to flow.
Voltage: The voltage is the same across every component in the circuit. (V_total = V₁ = V₂ = ...).
Current: The total current from the source is divided among the branches. The sum of the currents in each branch equals the total current. (I_total = I₁ + I₂ + ...).
Equivalent Resistance (Rₑₑ): The reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.
1/Rₑₑ = 1/R₁ + 1/R₂ + ...
Effect of Adding a Resistor: Adding another resistor in parallel decreases the total resistance and increases the total current from the source. This is how household outlets are wired; plugging in another appliance provides a new path for current.
Circuit Analysis
By combining these rules with Ohm's Law (V=IR), we can analyze circuits to find the voltage, current, and resistance for each component and for the circuit as a whole.