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ELC131_LAB_4_Series-Parallel.docx

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ELC 131 Lab 4: Series-Parallel and Bridge Circuits

Introduction: Virtually all electronic products are filled with components that are connected both in series and in parallel to form circuits that are coupled, or combined, in order to perform a desired function. The key component to analyzing series-parallel circuits is the ablility to recognize which components are connected in series and which components are connected in parallel.

Objectives: Upon completion of this lab exercise the student will be able to:

1. Identify which components are connected in series and which components are connected in parallel in a series-parallel circuit; calculate the total resistance of a simple series-parallel circuit.

2. Calculate and measure the current flow through and the voltage dropped across any component in a simple series-parallel circuit.

3. Calculate the node voltages of a ladder network.

4. Recognize a circuit as being a bridge configuration; determine the value of resistance that will balance a bridge circuit when the resistance of three arms is given.

5. Describe an operation of a bridge circuit used to sense a change in temperature.

Parts and Equipment: variable DC power supply and leads

DMM and meter leads

resistors, 1 W minimum: 360 Ω, 470 Ω, 680 Ω, 1 kΩ, 2.2 kΩ, 5.1 kΩ, 10 kΩ,

18 kΩ.

potentiometer, 25 kΩ

NTC thermistor, R0=10 kΩ

resistance substitution box

spring board and wires as needed

Prelab: Complete Section 1 Step 1 and Step 2.

Complete Section 2 Step 1.

Complete Section 3 Step 1.

Section 1: Series-Parallel Circuits

Before beginning the analysis of a series-parallel circuit, you must recognize which components are connected in parallel and which components are connected in series. Refer to the circuit of Figure 1. Resistors R2 and R3 are connected in parallel. Resistor R1 is in series with both the parallel combination of R2 and R3 and the source.

The current supplied by the source, IT, flows through R1. IT splits into two branch currents, IR2 and IR3, at node A. These two branch currents combine a node B and flow back into the source.

Figure 1: Series-Parallel Circuit Example

Calculating the total resistance is the first step in analyzing a series-parallel circuit. To find the total resistance of a series-parallel circuit, the circuit has to be simplified, one part at a time, until a simple series or a simple parallel circuit remains.

For the circuit of Figure 1, first the resistance of R2 in parallel with R3 is calculated as follows:

Now, the series-parallel circuit can be reduced to the simple series circuit shown in Figure 2.

Figure 2: Circuit of Figure 1 Reduced to a Series Circuit

The total resistance of the circuit of Figure 1 is calculated as follows:

The current supplied by the source is calculated using Ohm’s law as follows:

The voltage dropped across each of the resistors is calculated using Ohm’s law as follows:

The source current, IT, flows through R1.

The current through R2 is calculated using Ohm’s law as follows:

The current through R3 is calculated using Ohm’s law as follows:

Figure 3: Series-Parallel Circuit for Section 1

Step 1: Use the nominal values of the resistors to calculate the resistance of R2 in parallel with R3 and RT for the circuit of Figure 3. Record these values in Table 1.

Step 2: Calculate the current flow through each resistor and the voltage dropped across each resistor. Record these calculated values in Table 1.

Step 3: Use the DMM to measure the resistance of each resistor for the circuit of Figure 3. Record these measured values in Table 1.

Step 4: Connect resistors R2 and R3 in parallel. Measure the resistance of R2 in parallel with R3. Record this measured value in Table 1.

Step 5: Connect R1 in series with the parallel combination of R2 and R3. Measure the total resistance of the series-parallel configuration as shown in Figure 3. Record this measured value in Table 1.

Step 6: Construct the circuit in Figure 3. Measure the voltage dropped across each resistor and the current through each resistor. Record these measured values in Table 1. Turn off the power supply and disconnect the circuit.

Step 7: Calculate the percent error between the calculated values and the measured values. Record this data in Table 1.

Quantity	calculated	measured	% error
R1	360 Ω	366
R2	470 Ω	470
R3	680 Ω	717
R2R3	277.91
RT	673.91
IT = IR1	18mA	18.20
IR2	11mA	11mA
IR3	7mA	7.2mA
VR1	6.41V	6.74V
VR2= VR3	4.95V	5.25V

Table 1: Data for the Circuit of Figure 3

Section 2: Series-Parallel Ladder Network

A resistive ladder network is a series-parallel circuit configuration that is used to divide or scale down voltages. The circuit of Figure 4 is an example of a series-parallel ladder network.

Figure 4: Series-Parallel Ladder Network

Step 1: Using the nominal value of the resistors, calculate the voltages at nodes A and B for the circuit of Figure 4. Record these calculated values in Table 2.

Step 2: Construct the circuit of Figure 4. Measure the voltages at nodes A and B. Record these measured values in Table 2.

Step 3: Calculate the percent error between the calculated and measured values in Table 2. Record these values in Table 2.

Quantity	Calculated	Measured	% error
VA
VB

Table 2: Data for the Circuit of Figure 4

Section 3: Wheatstone Bridge Circuits

The Wheatstone bridge is used in the laboratory to make precision measurements of resistances. Also, the Wheatstone bridge is widely used in instrumentation circuits. The circuit of Figure 5 is an example of a Wheatstone bridge circuit. Frequently, a galvanometer is placed across the bridge. A galvanometer is an ammeter that can measure current flow in either direction.

A bridge circuit is considered to be balanced, or nulled, when the current through the galvanometer is zero. This occurs when the resistances in one arm (R1 and R2) of the bridge have the same ratio as the resistances in the other arm (R3 and R4) of the bridge. The bridge circuit of Figure 5 is balanced if:

Figure 5: Example of a Wheatstone Bridge Circuit

Unbalanced bridge circuits cannot be reduced to series-only or parallel-only circuits using the circuit reduction techniques described in Section 1. Unbalanced bridge circuits can only be analyzed by using a network analysis theorem, such as Thevenin’s theorem.

In this lab, instead of using a galvanometer, a DMM will be used as an ammeter. If the current through the ammeter is zero, the bridge is balanced.

Figure 6: Wheatstone Bridge Circuit for Section 3

Step 1: Use the nominal value of resistors to calculate the value of RX that will balance the bridge circuit of Figure 6. Record this value in Table 3.

Step 2: Construct the circuit of Figure 6 using the resistive decade box for RX. Set the resistive decade box to the value calculated in Step 1. Adjust the resistive decade box until the DMM reads 0.00 mA. Read the value of RX from the resistive decade box. Record this value in Table 3 as RX measured.

Step 3: Calculate the percent error between the calculated and measured values of RX and record this value in Table 3.

RX calculated	RX measured	% error
11124.12 Ω	11960Ω

Table 3: Data for the Circuit of Figure 6

Section 4: Wheatstone Bridge Application

Thermistors are widely used temperature sensors. The resistance/temperature relationship for NTC thermistors is described by the following equation:

where:

β values range from 1500 K to 7000 K. A typical β value is 4000 K. Figure 7 shows the response of an NTC thermistor, the A919a fluid temperature sensor.

Figure 7: A919a Fluid Temperature Sensor Resistance vs. Temperature

The circuit of Figure 8 shows a Wheatstone bridge circuit used as part of a temperature control system. The resistor labeled RT is an NTC thermistor.

Figure 8: Wheatstone Bridge Application

Step 1: Construct the circuit of Figure 8.

Step 2: Adjust the potentiometer, R2, until the voltmeter reads 0.00 V.

Step 3: Heat up the thermistor by holding it between your finger and thumb. Note the change in voltage.

Step 4: Cool the thermistor by holding it against a cold drink bottle (if available). Note the change in voltage.

Questions:

1. For the circuit of Figure 9, calculate the quantities listed below.

Figure 9

RT=

IT=

VR1=

VR2=

VR3=

IR1=

IR2=

IR3=

2. For the circuit of Figure 10, calculate the voltages at nodes A, B, and C.

Figure 10

VA =

VB =

VC =

3. For the circuit of Figure 11, calculate the values of R1, R2, and R3 necessary in order to provide the stated voltages and currents to Load 1, Load 2, and Load 3.

Figure 7

R1 =

R2 =

R3 =

4. For the circuit of Figure 12, complete the following:

Calculate the value of RX that will balance the bridge.

Calculate the current supplied by the source if the bridge is balanced.

Calculate the voltage dropped across RX if the bridge is balanced.

Figure 12

RX =

IS =

VRX =