Series-Parallel DC Circuits Lab EQUIPMENT REQUIRED Resistors 1-kΩ, . -kΩ, . -kΩ, . -kΩ Instruments DMM DC Power Supply Item / -W) Manufacturer And Model No. Laboratory Serial No. DMM Power Supply PROCEDURE Part 1: a) Construct the Series-Parallel Network. Insert the measured value of each resistor.  R1 Meas. = . KΩ  R2 Meas. = . KΩ  R3 Meas. = . KΩ R1 Cal . = . KΩ R2 Cal . = KΩ R3 Cal . = . KΩ b) Calculate the total resistance Rt using the measured resistance values and record it.  Rt = R1 + (R2//R3) Rt = . KΩ + Rt Calc. = . �Ω∗ . KΩ �Ω+ . �Ω ) KΩ Rt Meas. = 2.91KΩ c) Use the ohmmeter section of your multimeter to measure RT and record it. d) Determine the magnitude of the percent difference between the calculated and the measured values of parts 1(b) and 1(c) using the following equation and recorded. % � =| −� |∗ % =| % � . �Ω− . . �Ω �Ω Rt (Calculated) . |∗ % % Difference = 2.02% Rt (Measured) KΩ . % Difference KΩ 2.02% e) If 12V were applied, as shown in the Fig. Calculate the Currents Is, I 1, I2 and I3 using the measured resistor values and record it.  Is = It = I  Vt = It ∗ Rt V = It ∗ . KΩ � = . � KΩ It Calc. = 4.04mA It Meas. = 4.09mA     f) V =� ∗� V = . mA ∗ . KΩ V1 Calc.. = 8.89V V1 Meas. = 8.85V V2 Calc. = V3 = 3.11V V2 Meas. = 3.15V V I2 Calc. = 3.11mA I2 Meas. = 3.14mA � I3 Calc. = 0.94mA I3 Meas. = 0.95mA V = V = Vt − V V = V− . V I = I = V R . V I =R I = . KΩ . �Ω Apply 12 V, measure the currents I1, I2, I3 and Is using the milliammeter section of your multimeter, and record it. Be sure the meter is in series with the resistor through which the current is to be measured. Calculate the magnitude of the percent difference between calculated and measured values using the previews equation and enter in Table. % � � =| . ��− . �� � =| . �� . �� . �� . �� |∗ % � � =| . ��− . �� . ��− . �� % � � =| . ��− . �� % � |∗ |∗ |∗ % % Difference = 1.23% % % Difference = 0.96% % % % Difference = 1.23% % Difference = 1.06% The Currents Is and I1 are the same, because on a Series Circuit the Current is the same. In the circuit R1 is in Series with the Voltage Source, so the law is applied. Is Calculated 4.04mA Measured 4.09mA % Difference 1.23% I1 4.04mA 4.09mA 1.23% I2 3.11mA 3.14mA 0.96% I3 0.94mA 0.95mA 1.06% g) Using the results of part 1(e), calculate the voltages V1, V2 and V3 usind measured resistor values and record them.   V =� ∗� V = . mA ∗ . KΩ V1 Calc. = 8.89V V = V = Vt − V V = V− . V V2 Calc. = 3.11V h) Measure the voltages V1, V2 and V3, determine the magniuide of the percent difference between the calculated and measured values, and record the results in the table. % � % � % � � =| � =| � =| . �− . � . �− . � . �− . � . � . � . � |∗ % |∗ % |∗ % Difference = 0.45% % % Difference = 0.32% % Difference = 0.32% V1 Calculated 8.89V Measured 8.85V % Difference 0.45% V2 3.11V 3.10V 0.32% V3 3.11V 3.10V 0.32% On a Parallel Ccircuit the Voltage is the same. In the circuit, R2 is in pparallel with R3. So the Voltage is the same in both Resistors. i) Refering to the table. Does E = V1 + V2, as required by Kirchhoff Voltage law? Yes, the law is applied at those Voltages. PART 2: a) Construct the Serries-Parallel Network. Insert the measured value of each Resistor.  R1 Meas. = . KΩ  R2 Meas. = . KΩ  R3 Meas. = . KΩ R1 Cal . = . KΩ R2 Cal . = KΩ R3 Cal . = . KΩ b) Calculate the total resistance Rt using the measured resistor values and insert in Table.  Rt = R1 // (R2 + R3) Rt = . �Ω∗ . KΩ . �Ω+ . �Ω Rt = 1.46KΩ Rt Meas. = 1.43KΩ c) Use the ohmmeter section of your multimeter to measure the total Resistance RT and record it in the table. � =| % � . Rt (Calculated) . KΩ �Ω− . . �Ω �Ω |∗ % Rt (Measured) . KΩ % Difference = 0.45% % Difference 2.05% d) If 12V were applied to the Network, as shown in the Fig. Calculate the Currents Is, I 1, I2 and I3 using the measured Resistor values and insert in Table.   Is = It It = It = Vt Rt . V KΩ It Calc. = 8.22mA It Meas. = 8.3mA  I = I = V R V1 = E V . KΩ I1 Calc. = 5.45mA  I = I = It − I � =� = . I2 Calc. = 2.76mA I1 Meas. = 5.57mA �− . � I2 Meas. = 2.83mA e) Apply 12 V, measure the currents Is, I1, I2 and I3. Calculate the magnitude of the percent difference between calculated and measured values for each Current and record them in Table. % � % � % � % � � =| . ��− . �� . ��−. . �� � =| . ��− . �� . ��− . �� � =| � =| . �� . �� . �� . �� |∗ |∗ |∗ |∗ % % % % % Difference = 0.97% % Difference = 2.20% % Difference = 2.54% % Difference = 2.54% R2 an R3 are in Series, so the Current is the same in those Resistors by law. f) Refering to the Fig. Does Is = I1 + I2, as e ui ed y Ki hhoff s Cu e t Law? Yes, In the Circuit, R1 is in Parallel with R2. At the same time R2 is in Series with R3, Therefore I2 is the same as I3. Then, by definition, the sum of I2 + I1 is the Total Current of the Circuit. Calculated Measured % Difference Is 8.22mA 8.3mA 0.97% I1 5.45mA 5.57mA 2.20% I2 2.76mA 2.83mA 2.54% I3 2.76mA 2.83mA 2.54% g) Using the results of oart 2(d) and measured Resistor values, calculate the Voltages V 1, V2 and V3, and record in Table.    V1 = Vt = E = 12V � = � ∗� � = . � ∗ . �Ω V2 Calc. = 9.11V V2 Meas. = 9.23V V =I ∗R V = . V3 = 2.76V mA ∗ KΩ V3 Meas. = 2.81V h) Measure the Voltages V1, V2 and V3 and record them in Table. Calcule the magnitude of the percent difference between the calculated and the values for each Voltage and in sert in Table. % � % � % � � =| � =| � =| �− . � . �− . � . �− . � � . � . � |∗ |∗ % % Difference = 0.33% % % Difference = 1.81% |∗ % % Difference = 1.32% Calculated Measured % Difference V1 12V 12.04V 0.33% V2 9.11V 9.23V 1.32% V3 2.76V 2.81V 1.81% How are the Voltages E, V1 and the sum of V2 and V3 related? Use Table to detrermine the sum of V2 and V3. In the circuit R1 is in parallel with the Voltage Source, so by law in Parallel the Voltage is the same. Then E = V1. Also R2 and R3 are in Series. By definition, the sum of the Voltages are equal to the total Voltage, so V2 + V3 = Vt = E = V1 PART 3: a) Construct the Serries-Parallel Network and Insert the measured value of each Resistor.  R1 Meas. =  R2 Meas. =  R3 Meas. =  R4 Meas = . KΩ . KΩ‘3 . KΩ . KΩ R1 Cal R2 Cal R3 Cal R4 Cal .= .= .= .= . KΩ . KΩ . KΩ KΩ b) How the total Voltage across the two Series elements R1 and R2 elated to the applies Voltage E ? Why? Resistors R1 and R2 ar in series, so the Voltage in each Resistor is different. However, the equivalent Resistor formed by the sum pof R1 and R2 is in Parallel with The Voltage Source. It means, the Voltage of the two combinated Resistors V1 + V2 = E.  � = � + � // � + � � = . �Ω + . KΩ // . KΩ + KΩ � = �Ω // . KΩ KΩ∗ . KΩ Rt = �Ω+ . KΩ Rt Meas. = . Rt Calc. = 2.29KΩ  � � =� It = . V �Ω It Calc. = 6.99mA   � = � +� � =� KΩ It Meas. = 7.09mA = � +� = � =� � =� +�  � � +� =� � = . �Ω + . �Ω = �Ω � � = Then � = �  � = �� � � +� =� � = . �Ω + �Ω = . �Ω  � �Ω Then � = � � � =� =� = � � = � � = ��� . �Ω � =� =� = � How is the total Voltage across the two Series elements R3 and R4 related to the applied Voltage E ? Why? As the previous tworesistors, R3 and R4 are in Series, so the Voltage in each Resistor is different. By definition, the sum of the two Voltages V3 + V4 = E c) Using the conclusions of part 3(b), calculate the Voltages V2 and V4, using the Coltage Divider Rule and measured Resistor values in Table.      �� = �� � =� � � � � � = . �Ω V1 Calc. = 6.6V � =� � � V2 Calc.= 9.4V � � � � = �Ω V4 Calc. = 5V V1 Meas. = 6.64V V2 Meas. = 9.36V � V3 Calc. = 11V � =� �Ω � � = . �Ω �Ω � � = . �Ω � =� � . . �Ω V3 Meas. = 11.04V � . �Ω V4 Meas. = 5V d) Measure the Voltages V2 and V4 and recor them in Table. Calculate the magnitude of the percebt difference between calculated and measured values and insert them in Table. � =| % � . �− . � � . � % � � =| . �− . % � � =| �− � . � �− � =| % � � f) � = |∗ |∗ � |∗ % % Difference = 0.61% % % Difference = 0.36% % % % Difference = 0.43% % Difference = 0.0% Calculated Measured % Difference V2 9.4V 9.36V 0.43% V4 Vab 5V 4.4V 5V 4.36V 0% 0.91% Is 6.99mA 7.09mA 1.43% e) Usi g the esults of pa t it in Table.  . � |∗ , al ulate the Voltage Va , usi g Ki hhoff s Voltage Law a d e o d �− . � Vab Calc. = 4.4V Measure the Voltage Vab and determine the magnitude of the percent difference between the calculated and measured values and recor them in Table. % � � =| . �− . . � � |∗ % % Difference = 0.91% g) Is the Voltage Vab also equal to V3 – V1. Why? There are equal because the junctions are just right after the Resistor R 1 and R3 respectively. By definition, the Voltage of V1=Va, and also V3 = Vb h) Calculate the current Is, using any method you prefer. Use measured Resistor values and record in Table.  � =� = � � = . � �Ω Is = It = 6.99mA i) Measure the Current Is and calculate the magnitude of porcent difference between calculated and measured values and recor them both in Table.  � � =� It = . V �Ω It Calc. = 6.99mA It Meas. = 7.09mA PART 4: a) Construct the Serries-Parallel Network and Insert the measured value of each Resistor.  R1 Meas. =  R2 Meas. =  R3 Meas. =  R4 Meas = . KΩ . KΩ . KΩ 3.26 KΩ R1 Cal R2 Cal R3 Cal R4 Cal .= .= .= .= . KΩ KΩ . KΩ . KΩ b) Calculate the Voltage V4 using the measured Resistor values and insert the result in Table.   � = � + � // � + � � � +� ‘ = KΩ   =� Then � = � + � //� � � //� � = � ∗� � +� =� Then � = � + � Rt Calc. = . KΩ . � = �Ω Rd = 0.89KΩ KΩ Rt Meas. = . Ω       � = � = � = � = � +� +� � = � � Is Cal. = 6.47mA � = � ∗� � = . Is Meas. = 6.6mA � ∗ . �Ω V1 Calc. = 14.23V � = � −� = � � = �− V2 Calc. = 5.77V . � � =� +� = . � � � = . �Ω V4 Cal. = 2.38V . V2 Meas. = 5.81V � Vc = 5.77V � =� V1 Meas. = 14.19V V K�Ω V4 Meas. = 2.4V c) Measure the Voltage V4 and calculate the magnitude of the percent difference between calculated and measured values and record in Table. % � � =| . �− . � . � |∗ % % Difference = 0.84% d) Measure the Current Is and calculate the total input Resistance from � = Calculated Measured % Difference V4 2.38V 2.4V 0.84% Is 6.47Ma 6.6mA 2.01% Rt 3.09kΩ . KΩ � � and record in Table. 1.94% e) Disconnect the Power Supply and measure Rt using the Ohmmeter section of DMM. Then calculate the magnitude of the percent difference between the calculated and measured values. Record both results in Table. % � � =| . �Ω− . . �Ω �Ω |∗ % % Difference = 1.94% EXERCISES: 1. For the Series-Parallel Network determine V1, R1 and R2, using the information provided. Show all work! Assume Rint = 0Ω fo all ete s.   =� +� � = � ∗� For the first part R1//R2. Then I1//I2 Call R1//R2 = Ra    �+ �= �=� Now is a Series Circuit. So Ia = Is = 3mA � ∗� � =� +� � =� � � =� � = �. � = �. � �= . � � � � �= . �Ω �Ω �� � �� � R1 = . KΩ R2 = . KΩ