Series and Parallel Resistances

    Aim

     To find out the effective of the multiple resistances connected in series and parallel.

 

    Components

    Theory

1. Series Resistances

      When resistors are connected in series

• Same current flows through each resistor
• The voltage drop across each resistor will be different.
• The applied voltage is equal to the sum of the voltage drops across individual resistor.
• Voltage drops are additive, resistances are additive
• Powers are additive

     Total voltage applied,

     Where I is the current through the circuit and R is the total resistance of the circuit.

     Voltage drop across

     Voltage drop across

which is the equivalent series resistance.

1. Parallel Resistances

     When resistances are connected in parallel

• Same voltage acts across all resistors of the circuit
• Current flowing through each resistor varies.
• Branch currents are additive
• Conductances are additive
• Powers are additive.

      Power,

 

    Procedure

      EDWin 2000 -> Schematic Editor: The circuit diagram is drawn by loading components from the library. Wiring and proper net assignment has

      been made. The values are assigned for relevant components. The series and parallel resistance circuit diagrams in the Mixed mode simulator

      is shown below.

      EDWin 2000 -> Mixed Mode Simulator: The circuit is preprocessed. The desired test points and waveform markers are placed. The Transient

      Analysis parameters have been set. The Transient Analysis is executed. The test points display the values of the current through the resistors

      as shown.

      The variation of current through the two resistors with respect to variation in voltage is obtained by performing DC Sweep Analysis on both series

      and parallel resistance circuits. To perform DC Sweep Analysis a current waveform marker is placed. The sweep parameter (voltage) for input

      source is set in the Analysis window. The applied voltage is swept from an initial value of 0 to final value of 10V in steps of 100mV. The DC

      Sweep Analysis is executed and the corresponding waveforms are observed in the Waveform Viewer.

    Result

      The output waveform may be observed in the waveform viewer. The output waveforms of DC Sweep Analysis for series and parallel resistance

      circuits are shown below. From the graphs it is evident that the effective of the two similar resistances when connected in series will be greater

      compared to the case when they are connected in parallel.