Title:

Study of combination of series and parallel circuits and voltage sources are in series.

Introduction:

The series-parallel networks are networks that contain both series and parallel circuit configurations. The series circuit can be solved using the Kirchoff’s voltage law (KVL) and Voltage divider rule (VDR). The parallel circuit can be solved using the Kirchoff’s current law (KCL) and Current divider rule (CDR). The combination of series-parallel network can be solved using KVL, KCL, VDR and CDR. The purpose of this experiment is to:

1) Analyze the basic laws of series and parallel circuits.

2) Find the total circuit current of fixed circuit.

3) Observe the effect of two voltage sources in series.

Theory and Methodology:

Series Circuit:

A circuit consists of any number of elements joined at terminal points, providing at least one closed path through which charge can flow.Two elements are in series if

a) They have only one terminal in common (i.e., one lead of one is connected to only one lead ofthe other).

b) The common point between the two elements is not connected to another currentcarrying element.

Figure 1: Series Circuit

The current is the same through series elements. The total resistance of a series circuit is the sum of the resistance levels. In general, to find the total resistance of N resistors in series, the following equation is applied:

RT = R1+R2+R3+...........+RN (Ohms) I=E/RT (Amperes)

The voltage across each resistor using Ohm’s law; that is,

V1= IR1, V2= IR2, V3= IR3,........., VN= IRN (Volts)

Using KVL, E = V1 + V2

The voltage divider rule states that the voltage across a resistor in a series circuit is equal to the value of that resistor times the total impressed voltage across the series elements divided by the total resistance of the series elements. The following VDR equation is applied:

Vx=RxE/RT Similarly, V1=R1E/RT , V2=R2E/RT

Where, Vx is the voltage across Rx, E is the...