Series and Parallel Circuits

Section 1: Introduction to Series and Parallel Circuits

  • There are two fundamental ways of connecting components in circuits: Series and Parallel.
  • In a Series Circuit, all components are connected end-to-end along a single path so the same current flows through all of them.
  • In a Parallel Circuit, all components are connected across each other forming independent paths for the current to flow so that the voltage across each component is the same.

Section 2: Properties of Series Circuits

  • The total resistance (R_total) in a series circuit is equal to the sum of the individual resistances: R_Total = R_1 + R_2 + … + R_n.
  • The total current (I) in the circuit is the same through every component and is equal to the supply voltage (V) divided by the total resistance: I = V/R_Total.
  • The voltage across each component in a series circuit is different and depends on their resistances: V_1 = I * R_1, V_2 = I * R_2, … , V_n = I * R_n.
  • If one component fails in a series circuit, it breaks the entire circuit and all components will stop working because they are in the same pathway.

Section 3: Properties of Parallel Circuits

  • The total resistance in a parallel circuit is found using the formula: 1/R_Total = 1/R_1 + 1/R_2 + … + 1/R_n.
  • The total current in a parallel circuit is the sum of the currents through each pathway: I_Total = I_1 + I_2 + … + I_n
  • The voltage across each component in a parallel circuit is the same and is equal to the supply voltage: V = V_1 = V_2 = … = V_n.
  • If a component fails in a parallel circuit, the remaining components continue operating normally because the current can find alternate pathways.

Section 4: Combining Series and Parallel Circuits

  • In a Complex Circuit, series and parallel configurations can exist concurrently.
  • Total resistance can be calculated by reducing the circuit one stage at a time, treating series and parallel sections separately.
  • Similarly, current and voltage can be analysed by treating each simple series or parallel section in turn.

Section 5: Kirchhoff’s Laws

  • Kirchhoff’s Current Law (KCL) states that the sum of currents entering a junction equals the sum leaving it, a vital principle for understanding both series and parallel circuits.
  • Kirchhoff’s Voltage Law (KVL) states that the sum of voltages around any loop in a circuit equals zero, an important principle for analysing series circuits, and complex circuits involving both series and parallel sections.
  • Mastery of these laws brings understanding to real-world, complex electric circuits.