Serial Parallel Combination Circuits

OBJECTIVES

After performing this experiment, you will be able to:

1. Use the concept of equivalent circuits to simplify series-parallel circuit analysis.
2. Compute the currents and voltages in a series-parallel combination circuit and verify your computation with circuit measurements.

Resistors:
One 2.2 kΩ, one 4.7 kΩ,, one 5.6 kΩ, one 10 kΩ

SUMMARY OF THEORY

Most electronic circuits are not just series or just parallel circuits. Instead they may contain combinations of components. Many circuits can be analyzed by applying the ideas developed for series and parallel circuits to them. Remember that in a series circuit the same current is through all components, and that the total resistance of series resistors is the sum of the individual resistors. By contrast, in parallel
circuits, the applied voltage is the same across all branches and the total resistance is given by the reciprocals formula.

In this experiment, the circuit elements are connected in composite circuits containing both series and parallel combinations. The key to solving these circuits is to form equivalent circuits from the series or parallel elements. You need to recognize when circuit elements are connected in series or parallel in order to form the equivalent circuit.

For example, in Figure (a) we see that the identical current must go through both R2 and R3. We conclude that these resistors are in series and could be replaced by an equivalent resistor equal to their sum.

Figure (b) illustrates this idea. The circuit has been simplified to an equivalent parallel circuit. After finding the currents in the equivalent circuit, the results can be  applied to the original circuit to complete the solution.

1. The equivalent circuit you drew in step 3 is a simple series circuit. Compute the total resistance of this equivalent circuit and enter it in the first two columns of Table 10-2. Then disconnect the power supply and measure the total resistance to confirm your calculation.

2. The voltage divider rule can be applied directly to the series equivalent circuit to find the voltages across R₁, R_2,3, and R4. Find V₁, V_2,3, and V₄ using the voltage divider rule. Tabulate the results in Table in the Voltage Divider column.

3. Find the total current, I_T, in the circuit by substituting the total voltage and the total resistance into Ohm's law. Enter the computed total current in Table in the Ohm's Law column.

4. In the equivalent series circuit, the total current is through R₁, R_2,3, and R₄. The voltage drop across each of these resistors can be found by applying Ohm's law to each resistor. Compute V₁, V_2,3, and V₄ using this method. Enter the voltages in Table in the Ohm's Law column.