Laboratory Experiment No.1 Series RC and RL Circuits Agonia Maricris D PDF

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Laboratory Experiment No. 1 Series RC and RL CircuitsIntroductionBy definition, a circuit that contains pure resistance R ohms connected in series with a pure capacitor of capacitance C farads is known as RC Series Circuit sinusoidal voltage is applied and current I flows through the resistance (R) ...

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Laboratory Experiment No. 1 Series RC and RL Circuits

Introduction By definition, a circuit that contains pure resistance R ohms connected in series with a pure capacitor of capacitance C farads is known as RC Series Circuit.A sinusoidal voltage is applied and current I flows through the resistance (R) and the capacitance (C) of the circuit.On the other hand, RL Series Circuit is defined asa circuit that contains a pure resistance R ohms connected in series with a coil having a pure inductance of L (Henry). When an AC supply voltage V is applied, the current, I flow in the circuit. So, I R and IL will be the current flowing in the resistor and inductor respectively, but the amount of current flowing through both the elements will be same as they are connected in series with each other. So in this laboratory experiment, we will see and further analyze the concepts of series RC and RL circuits by conducting it with the given procedures; how the current and voltage work in this type of series circuit and how to measure the impedance of the RC and RL circuit.

Objectives The activity aims to: 1.

Familiarize with the series RC and RL circuits.

2.

Describe the relationship between current and voltage in a series RC and

RL circuit. 3.

Determine the impedance of a series RC and RL circuit.

4.

Measure properly the impedance of series and RC Circuit using measuring

instrument to compare the computed values to measure values

Material ● 100 w Lamp ● 5 uf Capacitor ● 1.389 H Inductor ● AC voltmeter ● AC ammeter ● AC supply ● Multisim Circuit Diagram

Figure 1. RC Circuit in Series

Figure 2. RL Circuit in Series Procedure:

A. RC Circuit a. Connect the circuit shown in Figure 1.

Figure 1 b. Measure the total current and the current across the lamp and across the 5 uf capacitor. To measure the total current of the AC voltage (refer to Figure 2A). Turn on the run button to simulate the circuit. Record the current reading for the AC voltage source. Repeat the step for to record the lamp and 5 uf capacitor as shown in Figure 2B and 2C.

Figure 2A

Figure 2B

Figure 2C c. Measure the voltage of the source (eT), lamp (eR) and the capacitor (eC). To measure the voltage across the source, refer to Figure 3A. Turn on the simulation to enable the reading. Record the reading foe the voltage across the source. Repeat the step to measure the voltage of the lamp and capacitor shown in Figure 3B and 3C.

Figure 3A

Figure 3B

Figure 3C

d. Using Ohm’s Law, compute the voltage and current for each component. Record it at Table 1 and 2. Use the formula 𝑒𝑅 𝑒𝑐 𝑒𝐿 𝑅 = ; 𝑋𝐿 = ; 𝑋𝐶 = 𝑖𝑐 𝑖𝐿 𝑖𝑅

𝑍=

𝑉𝑡 = √𝑅 2 + 𝑋𝑐2 𝐼𝑡

e. Compute the magnitude and phase angle of the impedance using the equation Z = R – jXc, where Xc = 1/2𝜋𝑓𝐶 . Use the 5 uF for the value of C. f. Compute the percent difference between the measure and the computed value of the impedance. B. RL Circuit a. Connect the circuit shown in Figure 4.

Figure 4 b. Measure the total current and the current across the lamp and across the 1.389 H inductor. To measure the total current of the AC voltage (refer to Figure 5A). Turn on the run button to simulate the circuit. Record the current reading for the AC voltage source. Repeat the step for to record the lamp and 1.389 H inductor as shown in Figure 5B and 5C.

Figure 5A

Figure 5B

Figure 5C

c. Measure the voltage of the source (eT), lamp (eR) and the inductor (eL). To measure the voltage across the source, refer to Figure 6A. Turn on the simulation to enable the reading. Record the reading for the voltage across the source. Repeat the step to measure the voltage of the lamp and inductor shown in Figure 6B and 6C.

Figure 6A

Figure 6B

Figure 6C d. Using Ohm’s Law, compute the voltage and current for each component. Record it at Table 1 and 2. Use the formula 𝑒𝑅 𝑒𝐿 𝑒𝑐 𝑅 = ; 𝑋𝐿 = ; 𝑋𝐶 = 𝑖𝑐 𝑖𝑅 𝑖𝐿

𝑍=

𝑉𝑡 = √𝑅 2 + 𝑋𝑐2 𝐼𝑡

e. Compute the magnitude and phase angle of the impedance using the equation Z = R + jXl, where Xl = 2 𝜋𝑓𝐿. Use the 1.389 H inductor for the value of L. f. Compute the percent difference between the measure and the computed value of the impedance.

Results and Discussions Following the step-by-step procedure, the figures below presents the total current, the current across the lamp as well as across the 5 uf capacitor in RC Circuit that was measured by the multimeter. As for the RL Circuit, the totalcurrent, the current across the lamp and across the 1.389 H inductor was also presented. The voltage across the source, lamp, capacitor (in RC) and inductor (in RL) was also presented together with the recorded values by the said measuring device.

Figure 3 below shows the total current of the AC Voltage in the given RC circuit diagram.

Figure3. RC Circuit in Series The figure above shows the circuit that was simulated to get the total current of the AC voltage in the given RC circuit diagram. As shown in the multimeter, the measured total current is 306.891 mA.

Figure 4 below shows the current reading across the lamp in the given RC circuit diagram.

Figure 4. RC Circuit in Series The figure above shows the circuit diagram that was simulated to get the current across the lamp in the given RC circuit diagram. As shown in the multimeter, the measured current across the lamp is 306.916 mA.

Figure 5 below shows the current reading across the 5-uf capacitor in the given RC circuit diagram.

Figure 5. RC Circuit in Series

The figure above shows the circuit diagram that was simulated to get the current across the5-uf capacitorin the given RC circuit diagram. As shown in the multimeter, the measured current across the5-uf capacitor is 306.891 mA.

Figure 6below shows the voltage reading across the source (eT) in the given RC circuit diagram.

Figure 6. RC Circuit in Series The figure above shows the circuit that was simulated to get the voltage of the source in the given RC circuit diagram. As shown in the multimeter, the measured voltage is 219.998V.

Figure 7below shows the voltage reading across the lamp (eR) in the given RC circuit diagram.

Figure 7. RC Circuit in Series The figure above shows the circuit that was simulated to get the voltage across the lamp in the given RC circuit diagram. As shown in the multimeter, the measured voltage is148.535V.

Figure 8 below shows the voltage reading across the capacitor (eC) in the given RC circuit diagram.

Figure 8. RC Circuit in Series The figure above shows the circuit that was simulated to get the voltage across the capacitor in the given RC circuit diagram. As shown in the multimeter, the measured voltage is 162.285V.

Figure 9 below shows the total current of the AC Voltage in the given RL circuit diagram.

Figure 9. RL Circuit in Series The figure above shows the circuit that was simulated to get the total current of the AC voltage in the given RL circuit diagram. As shown in the multimeter, the measured total current is 307.989 mA.

Figure 10 below shows the current across the lamp in the given RL circuit diagram.

Figure 10. RL Circuit in Series

The figure above shows the circuit that was simulated to get the current across the lamp in the given RL circuit diagram. As shown in the multimeter, the measured current across the lamp is 307.929 mA.

Figure 11 below shows the current across the 1.389 H inductor in the given RL circuit diagram.

Figure 11. RL Circuit in Series The figure above shows the circuit that was simulated to get thecurrent across the 1.389 H inductorin the given RL circuit diagram. As shown in the multimeter, the measured current across the 1.389 H inductor is 307.973 mA.

Figure 12below shows the voltage reading across the source (eT) in the given RL circuit diagram.

Figure 12. RL Circuit in Series The figure above shows the circuit that was simulated to get the voltage of the source in the given RL circuit diagram. As shown in the multimeter, the measured voltage is 219.997V.

Figure 13below shows the voltage reading across the lamp (eR) in the given RL circuit diagram.

Figure 13. RL Circuit in Series The figure above shows the circuit that was simulated to get the voltage across the lamp in the given RL circuit diagram. As shown in the multimeter, the measured voltage is 149.068V.

Figure 14below shows the voltage reading across the inductor (eL)in the given RL circuit diagram.

Figure 14. RL Circuit in Series The figure above shows the circuit that was simulated to get the voltage across the inductor in the given RL circuit diagram. As shown in the multimeter, the measured voltage is 161.818V.

The Table 1 below presents the resulting voltages of the series RC circuit through simulation and manual computation together with the percent difference of the impedance between the two.

Table 1: Simulation and Computation Result of the Voltage of the Series RC Circuit Voltage (V)

Lamp (R)

Capacitor (C)

Total

Workbench

148.535V

162.285V

219.998V

Computation

148.104V

162.338V

219.746V

% Difference

0.29%

0.03%

0.11%

As shown, this Table 1 shows the results of measured and computed voltage of the lamp(R), capacitor(C), and the total voltage of the given series RC circuit performing the simulation and the manual computation. After turning on the run button to simulate the circuit, the lamp has recorded a voltage of 148.535V; on the other hand the resulted value of the voltage of the lamp in manual computation is 148.104V. The percentage difference between these two is 0.29% which only means that since they are so close, the difference is so small. Next is for the capacitor, as shown in the table the simulated value is 162.285V while its computed value is 162.338V. The percentage difference between these two is 0.03%. Lastly, the resulted total voltage of the given circuit through simulation is 219.998V while in manual computation the resulted total voltage is 219.746V. The yielded percentage difference is 0.11%.

The Table 2 below presents the current of the series RC circuit through simulation and manual computation together with the percent difference of the impedance between the two.

Table 2: Simulation and Computation Result of the Current of the Series RC Circuit Current(A)

Lamp (R)

Capacitor (C)

Total

Workbench

0.307A

0.307A

0.307A

Computation

0.306A

0.306A

0.306A

% Difference

0.33%

0.33%

0.33%

As shown, this Table 2 shows the results of measured and computed current of the lamp(R), capacitor(C), and the total current of the given series RC circuit performing the simulation and the manual computation. We can see that either in simulation or computation, the value of the lamp, capacitor, and the total current is 0.307A. In results, the percentage difference was recorded also the same which is 0.33% which only means that the difference between the two is so small.

The Table 3 below presents the resulting voltages of the series RL circuit through simulation and manual computation together with the percent difference of the impedance between the two.

Table 3: Simulation and Computation Result of the Voltage of the Series RL Circuit Voltage (V)

Lamp (R)

Inductor (L)

Total

Workbench

149.068V

161.818V

220V

Computation

149.556V

161.805V

219.997V

% Difference

0.33%

0.008%

0.001%

As shown, this Table 3 shows the results of measured and computed voltage of the lamp(R), inductor (L), and the total voltage of the given series RL circuit performing the simulation and the manual computation. After turning on the run button to simulate the circuit, the lamp has recorded a voltage of 149.068V; on the other hand the resulted value of the voltage of the lamp in manual computation is 149.556V. The percentage difference between these two is 0.33% which only means that since they are so close, the difference is so small. Next is for the inductor, as shown in the table the simulated value is 161.818V while its computed value is 161.805V. The percentage difference between these two is 0.008%. Lastly, the resulted total voltage of the given circuit through simulation is 220V while in manual computation the resulted total voltage is 219.997V. The yielded percentage difference is 0.001%.

The Table 4 below presents the current of the series RL circuit through simulation and manual computation together with the percent difference of the impedance between the two.

Table 4: Simulation and Computation Result of the Current of theSeries RL Circuit Current(A)

Lamp (R)

Inductor (L)

Total

Workbench

0.308A

0.308A

0.308A

Computation

0.309A

0.309A

0.309A

% Difference

0.32%

0.32%

0.32%

As shown, this Table 4 shows the results of measured and computed current of the lamp(R), inductor (L), and the total current of the given series RL circuit performing the simulation and the manual computation. We can see that either in simulation or computation, the value of the lamp, inductor, and the total current is 0.308A. In results, the percentage difference was recorded also the same which is 0.32% which only means that the difference between the two is so small.

Conclusion

After conducting and thoroughly analyze the results of the experiment, I clearly understand the relationship between the current and voltage in a series RC and RL circuit. Connected in series, the current that passing through RC and RL circuits have a voltage that is constant. I therefore conclude that base on the experimentit is correct that the behavior of current and voltage in RC and RL circuit is the same as the circuit that only have a resistor and theonly difference is that the RL circuit leads while the RC circuit is lagging.I was also able to familiarize on how to determine the impedance of both RC and RL circuits. It follows the same way but it only differs in the values that will begoing to use. In this experiment, I also notice that there is a small percent of difference between the measure impedance through simulation and the calculated impedance. I also familiarize myself that Capacitance belongs to RC circuit and Inductance belongs to RL circuit. One thing that I also noticed is that it is very important for us to know the fundamental laws and its concepts for us to get and solve what is needed in a certain problem. Like in every other experiment, in this experiment Ohm’s Law was still use to compute for certain values like the resistance.

Analysis A. Questions a. Do the workbench and computational values of voltages and currents agree? 

Yes, though there is a small discrepancy between the workbench and computational values we can see that the resulted values of voltages and currents do agree.

b. Give possible reasons for any discrepancies. 

First, maybe because we are rounding off the numbers in computing for another set-up



Second, maybe because the computations in simulation resulted an exact value that differs from the manual computation

B. Circuit Design a. Draw a series RC circuit design that has 100 W lamp and connected to 220 V, 60 cycle and consist of capacitor C. The capacitive reactance is 884.1941 ohms and total impedance is 1007.9956 ohms. Calculate the value of R and C.

b. Design a RL circuit which has a total impedance of 685.0844 ohms and series with a 100 W, when the circuit is connected to 220 V, 60 cycles. Find the inductance of an inductor.

C. Problems

a. What value of resistance should be placed in parallel with a 50 uF capacitor in order to have a total power factor of 0.8 on a 60 cycle AC system?

b. A pure capacitor and a pure resistor are connected in series in an AC circuit. A voltmeter reads 30 V when connected across the capacitor and 40 V when connected across the resistor. What will it read when connected across both?

c. A current of 2.5A is observed in 120 V 60 Hz circuit which consists of pure resistor and pure inductor in series. The voltage across the resistor and inductor are found to be identical. Calculate the value of the resistance and inductance.

Manual Computation To check further if the obtained values were correct and accurate and to verify the experimental results, here is the manual computation.

The figure below presents themanual computation for capacitive reactance, resistance, and impedance in the given RC circuit diagram.

Figure 18. RC Circuit Computation As shown on the computation, the value of capacitive reactance (XC) was obtained through the values of frequency and capacitance. The frequency has a value of 60 Hz while the capacitance has the value o f 5µf. Applying the formula, the value obtained for capacitive reactance is 530.516Ω. Next is the resistance (R) which is obtained by using the values of the resistor of the circuit which is the lamp and so the obtained resistance is 484Ω. Lastly is the impedance (z), it is the square root of the sum of the squares of the capacitive reactance and resistance. Finally, the obtained value for the impedance is 718.125Ω or 484-j530.516.

The figure below presents the manual computation for the total current in the given series circuit, the voltage drop in the resistor and conductor, the total voltage and the and phase angle of the impedance using the given formula in the given RC circuit.

Figure 19 As shown in the computation, the total current was obtained using the formula. The current remains constant because the circuit is connected in series. The computed total current is 0.306A. Next is the computation for the voltage across the lamp. It is computed by simply multiplying the current and resistance of the lamp. The obtained value is 148.104V. The next one is the voltage drop of the capacitance which can be obtained by simply multiplying the current and the resistance of the capacitor. The obtained value is 162.338V. Then the total

voltage was also computed by the given formula. The total voltage obtained is 219.746V. Lastly, the phase angle of the impedance was also computed using the given formula. As shown, the angle obtained is 47.63°.

The figure below presents the computation for the percentage difference in the impedance between the measure and the computed value of the current in the given RC circuit.

Figure 20 As shown on the computation, the percentage difference was computed by simply substituting the values of theoretical and experimental in the formula multiply by 100. The obtained value of percentage difference in the current of the given circuit is 0.33%.

The figure below presents the computation for the percentage difference in the impedance between the measure and the computed value of the voltage across the resistor and conductor, and in total voltage.

Figure 21 As shown on the comp...