ame & Surname: D: Date: EEE 20 Circuit Theory - Laboratory Kirchoff s Laws, Series-Parallel Circuits List of topics for this laboratory: Ohm s Law Kirchoff s Current Law(KCL) Kirchoff s Voltage Law(KVL) Series and Parallel esistors Tools and Equipments equired: DMM(Digital Multi Meter) esistors Breadboard DC power supply nformation: Ohm s Law states that the voltage v across a resistor is directly proportional to the current i flowing through the resistor. v i (.) The resistance of an element denotes its ability to resist the flow of electric current; it is measured in ohms ( Ω ). A resistor is either fixed or variable. Most resistors are of the fixed type, meaning their resistance remains constant. Variable resistors have adjustable resistance. A common variable resistor is known as potentiometer or pot for short. The pot is a three terminal element with a sliding contact or wiper. Figure. Circuit symbol for: (a) a variable resistor in general (b) potentiometer EEE 20 Circuit Theory Page of 9
A resistor that obeys Ohm s Law is known as linear resistor. A non-linear resistor does not obey Ohm s Law. A useful quantity in circuit analysis is the reciprocal of resistance, known as conductance and denoted by G. i G (.2) v A branch represents a single element such as a voltage source or resistance. A node is the point of connection between two or more branches. A loop is any closed path in a circuit. Figure.2 odes, branches and loops A network with b branches, n nodes and l independent loops will satisfy the fundamental theorem of network topology. b l + n (.3) Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current. Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them. Figure.3 Series and parallel connections Kirchoff s Current Law(KCL) states that the algebraic sum of currents entering a node(or a closed boundary) is zero. EEE 20 Circuit Theory Page 2 of 9
i n n For a node: 0 (.4) Kirchoff s Voltage Law(KVL) states that the algebraic sum of all voltages around a closed path(or loop) is zero. v n n For a loop: 0 (.5) The equivalent resistance of any number of resistors connected in series is the sum of the individual resistances. eq + 2 + 3 +... + n (.6) n The equivalent resistance of two parallel resistors is equal to the product of their resistances divided by their sum. + + +... + (.7) eq 2 3 f... 2 3 then eq (.8) Preliminary Work: ) Solve the network (find all the voltage drops and currents) of figure.4 for the given values of K, 2.8K, 3 3.3K, V 0 volts,v2 0 volts. - You can calculate voltage drop with this formula :, Vc Va gives the voltage drop. You can measure the voltages for each node (node a, c, d) respect to the reference node (node b). Then the voltage drop on 3 can be calculated like that; V 3 Va Vb (if we choose node b as ground than Vb 0) Figure.4 EEE 20 Circuit Theory Page 3 of 9
2) Calculate the equivalent resistance ab in figure.5. Figure.5 3) Solve the network (find all the voltage drops and currents) of figure.6. Figure.6 EEE 20 Circuit Theory Page 4 of 9
Procedure: ) Setup the circuit of figure.7 to measure the resistance of a resistor. nitially, set Vr 0 to its minimum value using the potentiometer. Then vary the rheostat position so that the value of Vr is 0, 3, 6, and 9 volts, in turn. For each case measure and record r. Then plot vs. V graph and determine the resistance. (Plot it to graph.) Figure.7 Graph. EEE 20 Circuit Theory Page 5 of 9
2) Construct the network of figure.8 for the given values of K, 2.8K, 3 3.3K, V 0 volts,v2 0 volts. Figure.8 3) Calculate the voltage drops and currents on each resistance (for, 2, 3) with Kirchoff s rules(kvl and KCL) and write them to table.. (You can use the values which you find in preliminary work ) Voltage drop Current V 2 V 2 2 3 V 3 3 Table. 4) Measure the voltage drops and currents on each resistance (for, 2, 3) and write them to table.2. Voltage drop Current V 2 V 2 2 3 V 3 3 Table.2 EEE 20 Circuit Theory Page 6 of 9
5) Construct the ladder network of figure.9. Calculate and measure the equivalent resistance ab. Write the values to table.3. Figure.9 Calculation Measurement ab Table.3 6) Measure the currents and voltage drops for, 2, 3, 4, 5, 6 in figure.0 and write them to table.4 Figure.0 EEE 20 Circuit Theory Page 7 of 9
Voltage drop Current 2 3 4 5 6 Table.4 7) A resistor ladder /2 circuit is an application of series-parallel circuits which is mostly used in DAC (Digital to Analog Conversion). Construct the /2 circuit in figure. and measure the Vout values for different combination of switches. Write the values to table.5. (Closed 2 volts, opened ground) Vout Switch is closed, others opened Switch2 is closed, others opened Switch3 is closed, others opened Switch4 is closed, others opened Table.5 EEE 20 Circuit Theory Page 8 of 9
Figure. After Lab: ) Construct circuits in figure.0 and. in Multisim. 2) E-mail them to gorkem.serbes@bahcesehir.edu.tr. EEE 20 Circuit Theory Page 9 of 9