5.3.2 Series & Parallel Circuits

Current

• In a series circuit, the current is the same for all components
• In a parallel circuit, the current is split across the different branches (or junction). The total current into a junction must equal the total current out of a junction
  • The amount of current in each branch depends on the total resistance of the components within that branch

Potential Difference

• In a series circuit, the e.m.f of the power supply is shared amongst all the components in different amounts, depending on their resistance
• In a parallel circuit, the voltage of all the components in each branch is equal to the e.m.f of the power supply

• Cells can also be connected in series or parallel
• The total voltage of the combined cells can be calculated in the same way as voltage
  • If the cells are connected in series, the total voltage between the ends of the chain of cells is the sum of the potential difference across each cell
  • If the cells are connected in parallel, the total voltage across the arrangement is the same as for one cell

• A summary of the current, voltage and resistance within a series and parallel circuit are summarised below:

Table of Voltage, Current & Resistance in Series & Parallel Circuits

Conservation of Charge

• Charge is never used up or lost in a circuit - this is known as conservation of charge
• As a result of this, for current in a parallel circuit:

The sum of the currents entering a junction always equal the sum of the currents out of the junction

• This is sometimes known as Kirchhoff's First Law
• In a circuit:
  • A junction is a point where at least three circuit paths meet
  • A branch is a path connecting two junctions

• If a circuit splits into two branches, then the current before the circuit splits should be equal to the current after it has split
• In the circuit below, I = I₁ + I₂+ I₃, where I represents the current in the circuit before it branches, and I₁, I₂ and I₃ represent the current in the respective three branches:

The current I into the junction is equal to the sum of the currents out of the junction

• The charge is conserved on both sides of the junction
• In a series circuit, the current is the same through all components

The current is the same at each point in a series circuit

• In a parallel circuit, the current divides at the junctions and each branch has a different value
• Kirchhoff’s First Law applies at each junction

The current divides at each junction in a parallel circuit

Conservation of Energy

• Energy is never used up or lost in a circuit - this is known as conservation of energy
• As a result of this, for voltage in any circuit:

The total e.m.f. in a closed circuit equals the sum of the potential differences across each component

• This is sometimes known as Kirchhoff's Second Law
• Each closed circuit can be treated like a series circuit
• Below is a circuit explaining Kirchhoff’s Second Law with the sum of the voltages in the closed series circuit equal to the total e.m.f:

The sum of the voltages is equal to the total e.m.f from the batteries

• In a series circuit, the voltage is split across all components depending on their resistance
  • The sum of the voltages is equal to the total e.m.f of the power supply

• In a parallel circuit, the voltage is the same across each closed loop
  • The sum of the voltages in each closed circuit loop is equal to the total e.m.f of the power supply:

The sum of the e.m.fs in each closed loop is equal to the total e.m.f of the power supply

• A closed-circuit loop acts as its own independent series circuit and each one separates at a junction. A parallel circuit is made up of two or more of these loops

Each circuit loops acts as a separate, independent series circuit

• This makes parallel circuits incredibly useful for home wiring systems
  • A single power source supplies all lights and appliances with the same voltage
  • If one light breaks, voltage and current can still flow through for the rest of the lights and appliances