UNIVERSITY OF TURKISH AERONAUTICAL ASSOCIATION DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EEE203 ELECTRONIC CIRCUITS LABORATORY I FALL 2014/2015 LAB 2: RESISTORS ASSOCIATION AND THE WHEATSTONE BRIDGE Preliminary Reading There are different forms of connecting resistors in a circuit: Series connected resistors. Parallel connected resistors. Series-Parallel connected resistors. 1. Resistors Connected in Series A circuit composed solely of components connected in series is known as a series circuit. In a series circuit, the current through each of the components is the same, and the voltage across the circuit is the sum of the voltages across each component. The total resistance (the equivalent resistance) of resistors in series is equal to the sum of their individual resistances: Figure 1 2. Resistors Connected in Parallel A circuit composed solely of components connected in parallel is known as a parallel circuit. In a parallel circuit, the voltage across each of the components is the same, but the current is different. The total current is the sum of the currents through each component. The total resistance (the equivalent resistance) of resistors in parallel is calculated as follows:
Figure 2 3. Mixed Connected Resistors (Series-Parallel) In practice, the circuits are not as simple as the ones mentioned above, because as a general rule resistors are fitted in series-parallel groups, that is, one or several resistors are found in series with a parallel circuit. These circuits are called mixed circuits. To solve these circuits, the series and parallel assemblies which constitute it are solved independently, transforming the parallel resistors by blocks into an equivalent form and associating them with the rest of the circuit. 4. The Wheatstone Bridge Figure 3 The set constituted by four resistors R1, R2, R3 and Rg as it is shown in Figure 4 is called the Wheatstone Bridge. Figure 4
The points B and D are joined by a voltmeter, which will measure the potential difference between the two points. Supposing the voltmeter points to 0 volts, it indicates that the voltage between the points A and B is equal to the voltage between the points A and D, consequently, the following equations are carried out: V B V A = V D V A V C V B = V C V D V B V A = I 2 R 2 I 2 R 2 = I 3 R 3 V D V A = I 3 R 3 V C V B = I 1 R 1 I 1 R 1 = I 4 R g V C V D = I 4 R g We also know that, as the potential difference between the points B and D is zero, then: I 1 = I 2 I 3 = I 4 Dividing the two members of these equations reciprocally; Or R 1 R 3 = R 2 R g that is, when the voltmeter points to zero volts, the product of two opposite resistors is equal to the product of the other two. Then, if from the four resistors, three are known, the fourth one is known as well. 1. The Wheatstone Bridge In a typical Wheatstone bridge, four resistors are positioned in a circuit designed in such a way that the current from a power supply splits, flows through the sequence of resistors, then recombines into a single conductor. Three of these resistors have known values, one of which is variable, or adjustable. The value of the fourth resistor is not known. By studying and manipulating the paths the current can take through the Wheatstone bridge grid, that fourth, unknown resistance can be identified.
To carry out this practice we will use the circuit printed as Circuit #5, shown in Figure 3. Figure 3 We will use the Wheatstone Bridge to calculate the value of the resistors Ra. Measure the value of resistors Ra with the ohmmeter. Write down the resistor value. As we have seen in the theory, when the voltmeter indicates zero, a relationship among the four resistors of the bridge is produced. We will try to make the current equal to zero and take advantage from the relation among the four resistances. We apply voltage to the board with the switch of the base unit. With the potentiometer of +9 volts we can change the voltage applied to the Wheatstone bridge. If the voltmeter does not point to 0 volts, varying the potentiometer of the circuit Circuit #5 Ra, we can make the current and voltage equal to zero. In that moment the relationship among the four resistors can be applied. Q1: What is the measured value for the potentiometer resistance, Ra? Q2: What is the calculated value of resistor Ra? Show your calculations.
Q3: Repeat all the steps for a voltage of 7-V. Find Ra. Does the calculated resistance Ra depend on the voltage we apply to the circuit? Q4: If we place three resistances in parallel of values 1500, 2700 and 1000 ohms. What is the value of the equivalent resistance of the group (in ohms)? Q5: What is the equivalent resistance of the circuit ( + series, parallel )? A.- R1+(R2 R3 R4) B.- R1+(R2+(R3 R4)) C.- R1+(R3 (R2+R4)) D.- R1 (R2+R4) R3