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Study of transient response of RC and RL circuit.
Typology: Lab Reports
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(^4) Lab 2 : Study of the Transient Response of RC and RL Circuits
2. Applied 5 volt PULSE and 20kHz frequency from function generator. 3. Attach the nobs of oscilloscope to input and ground of the circuit and across the inductor or capacitor. 4. We get two wave forms one input and other for output. 5. We determine the steady state condition using cursor then counted the time by counting the boxes. 6. We repeated the same process with resistance values 3k and 5 k ohm and observe the response.
2.6.1 RC Circuit:
1. Circuit: Figure 2 : Series RC circuit, capacitor and resistor in series, from experiment. 2. Output waveforms from oscilloscope: Below are the plot of voltage across capacitor at different values of resistance. Figure 2. 3 : Plot of voltage across capacitor, R = 1 KΩ
5 Figure 2. 4 : Plot of voltage across capacitor, R = 3KΩ Figure 2. 5 : Plot of voltage across capacitor, R = 5KΩ
3. Observation table: Resistance (KΩ) Time for full charge Theoretical (s) Time for full charge Simulation (s) Time for full charge Experimental (s) Deviation - Theory and Simulation (%) Deviation - Theory and Experimental (%) 1 53u 55u 52u 3.77 1. 3 159u 157u 176u 1.26 10. 5 265u 267u 256u 0.75 3. Table 2. 1 : Experimental results for RC circuit. **2.6.2 RL Circuit:
7 Figure 2. 8 : Plot of current through inductor, R = 3KΩ Figure 2. 9 : Plot of current through inductor, R = 5KΩ
3. Observation table: Resistance (KΩ) Time to reach final value Theoretical* (s) Time to reach final value Simulation (s) Time to reach final value Experimental (s) Deviation - Theory and Simulation (%) Deviation - Theory and Experimental (%) 1 250u 252u 204u 0.8 19 3 83u 80u 72u 3.6 13 5 50u 54u 40u 8 20 Table2. 2 : Experimental results for RL circuit. *Calculations are done in appendix.
In this experiment we analyzed the transient response of RC and RL circuit. And compared the time in theory, simulation and experiment and find large errors in results. Major reason for these errors was the unavailability of desired equipment such as we need 3k ohm resistor but we find 3.3k ohm, we needed 47mH inductor but we got 60mH inductor, which was closest to the theory value. The tolerance of the components also contributed to the errors. We were measuring the results from oscilloscope that has maximum voltage resolution of 20mV hence error expected. Due to these factors the deviation between
(^8) Lab 2 : Study of the Transient Response of RC and RL Circuits simulation and theory is very less as compared to the theory and experiment. Both the RL and RC circuits requires approximately 5 time constants to reach final values.
In this experiment we were taught about the use of oscilloscope and way to determine the transient response using oscilloscope. We learned about how to fed the circuit from function generator. This very informative and full of concepts of RC and RL circuits specially in transient analysis.
2.9.1 Simulation Results:
1. RL Circuit: Figure 2. 10 : Series RL Circuit Diagram Simulation: With R=1K:
(^10) Lab 2 : Study of the Transient Response of RC and RL Circuits Figure 2. 14 : Time (t) at Current (IL1) = 1.66mA With R=5K: Figure 2. 15 : Current through inductor L1 with R = 5K Figure 2. 16 : Time (t) at Current (IL1) = 0.99mA
2. RC Circuit: Figure 2. 17 : Series RC Circuit Diagram
11 Simulated Results: With R = 1k: Figure 2. 18 : Voltage across capacitor, R = 1K Figure 2. 19 : Time (t) at Voltage (Vc1) = 4. With R = 3K:
13 Figure 2. 23 : Time (t) at Voltage (Vc1) = 4. 2.9.2 Theoretical Calculations
1. RL Circuit: Maximum value of current through inductor is given by; iL1(∞) = Vs R 1 For R = 1K; iL1(∞) =
= 5mA For R = 3K; iL1(∞) =
= 1.6667mA For R = 5K; iL1(∞) =
= 1mA Now the time (t) required by the inductor to reach its maximum value is approx. 5 time constants i.e. 5 τ where τ = L R
Now for calculating t we use eq: VC(t) = VC(∞) + (VC(0) − VC(∞))𝐀 −(t) τ (^) (2.1) 4.99 = 5 + (0 − 5)𝐀 −(t) τ t = 6.215 × τ (2.2) For R = 1K; τ =
47m 1K = 47μs Using eq. ( 2 .2) t = 6.125 × τ = 6.125 × 47 μ = 292 μs For R = 3K; τ =
47m 3K = 15.6667 μs Using eq. ( 2 .2) t = 6.125 × τ = 6.125 × 15.6667 μ = 97 μs For R = 5K; τ =
47m 5K = 9.4μs Using eq. ( 2 .2) t = 6.125 × τ = 6.125 × 9.4μ = 58 μs
2. RC Circuit: Maximum value of voltage across capacitor C1 is given by; vC1(∞) = Vs For R = 1K, 3K and 5k: vC1(∞) = 5 Now the time (t) required by the capacitor to reach its maximum value is approx. 5 time constants i.e. 5 τ where τ = RC; Now for calculating t we use eq: VC(t) = VC(∞) + (VC(0) − VC(∞))𝐀 −(t) τ (^) (2.3) 4.99 = 5 + (0 − 5)𝐀 −(t) τ t = 6.215 × τ (2.4) For R = 1K;
(^14) Lab 2 : Study of the Transient Response of RC and RL Circuits τ = RC = 1K × 0.01μ = 10μs Using eq.(2.4) : t = 6.125 × 10 μ = 62.14μ For R = 3K; τ = RC = 3K × 0.01μ = 30μs Using eq. ( 2 .4) : t = 6.125 × τ = 6.125 × 30 μ = 186 μs For R = 5K; τ = RC = 5K × 0.01μ = 50μs Using eq. ( 2 .4) : t = 6.125 × τ = 6.125 × 50 μ = 310 μs
