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RL and RC Circuits Time Constant Objective The DC steady state response of simple RL and RC circuits is examined. The transient behavior of RC circuits is also tested. Theory Overview The DC steady state response of RL and RC circuits are essential opposite of each other: that is, once steady state is reached, capacitors behave as open circuits while inductors behave as short circuits. In practicality, steady state is reached after five time constants. The time constant for an RC circuit is simply the effective capacitance times the effective resistance, r = RC. In the inductive case, the time constant is the effective inductance divided by the effective resistance, r = L/R. Equipment (1) DC power supply (1) DMM (1) Stopwatch Components (1) 50 MF (1) 470 HF (1) 4.7 mH (2) 1 kQ (2) 100 kSINE Schematics thistento9 28 bas 19 E L evilbetdo Figure 1.1 R1 E SR2 C LET Ineragings Figure 1. 2 Procedure RL Circuit ainenoumod 1. Using figure 1.1 with E=10 V, R=100 k$2 and L=4.7 mH, calculate the time constant and record it in Table 1.1. Also, calculate and record the expected steady state inductor voltage in Table 1.2. 2. Set the power supply to 10 V but do not hook it up to the remainder of the circuit. After connecting the resistor and inductor, connect the DMM across the inductor set to read DC voltage (20 volt scale). 3. Connect the power supply to the circuit. The circuit should reach steady state very quickly, in much less than one second. Record the experimental inductor voltage in Table 1.2. Also, compute and record the percent deviation between experimental and theory in Table 1.2. 2RC Circuit 4. Using figure 1.2 with E=10 V, R1=1 k, R2=1 k and C=50 JF, calculate the time constant and record it in Table 1.3. Also, calculate and record the expected steady state capacitor voltage in Table 1.4 . 5. Set the power supply to 10 V but do not hook it up to the remainder of the circuit. After connecting the resistors and capacitor, connect the DMM across the capacitor set to read DC voltage (20 volt scale). 6. Connect the power supply to the circuit. The circuit should reach steady state quickly, in under one second. Record the experimental capacitor voltage in Table 1.4. Also, compute and record the percent deviation between experimental and theory in Table 1.4. RC Circuit (long time constant) 7. Using figure 1.2 with E=10 V, R1=100 k$2, R2=100 k$2 and C=470 uF, calculate the time constants and record them in Table 1.5. Also, calculate and record the expected steady state capacitor voltage (charge phase) in Table 1.5. 8. Set the power supply to 10 V but do not hook it up to the remainder of the circuit. After connecting the resistors and capacitor, connect the DMM across the capacitor set to read DC voltage (20 volt scale). 9. Energize the circuit and record the capacitor voltage every 10 seconds as shown in Table 1.6. This is the charge phase. 10. Disconnect the power supply from the circuit and record the capacitor voltage every 10 seconds as shown in Table 1.7. This is the discharge phase. 1 1. Using the data from Tables 1.6 and 1.7, create two plots in Excel of capacitor voltage versus time and compare them to the theoretical plots below. Vo Charging 0.632 Vo 0.368 V Discharging 3\fQuestions 1. What sorts of shapes do the charge and discharge voltages of DC RC circuits follow? Write down the equations that describe the charge and discharge voltages across the capacitor. 2. After one time constant, what is the value of the voltage across the capacitor from your plots (charge and discharge)? Compare both values to the theoretical values by calculating the percent deviation. 3. What sorts of shapes do the voltage of DC RL circuit follow? Write down the equation that describe the voltage across the Inductor. 4. For the RL circuit when t = 3t (a) How much energy is delivered by the power supply? (b) How much of this energy is stored in the magnetic field of the inductor? (c) How much of this energy is dissipated in the resistor? 5. For the RC circuit when t = 3t (a) How much energy is delivered by the power supply? (b) How much of this energy is stored in the electric field of the capacitor? (c) How much of this energy is dissipated in the resistor