Exercise 1: RC EXERCISE OBJECTIVE When you have completed this exercise, you will be able to determine the time constant of an RC circuit by using calculated and measured values. You will verify your results with an oscilloscope. DISCUSSION A capacitor opposes change in voltage, an inductor opposes change in current, and a resistor opposes current whether it is changing or not. The time constant of a circuit is the amount of time required for current in an inductive circuit or for voltage in a capacitive circuit to reach approximately 63 percent of its maximum value. The time constant ( ) of an RC circuit depends on the values of R (resistance) and C (capacitance): = R x C In the formula above, equals time in seconds, R equals resistance in ohms, and C equals capacitance in farads. What is the time constant of the RC circuit shown? = R x C = ms (Recall Value 1) When the switch is closed (assuming there is no initial charge on the capacitor), the voltage across C1 (V C1 ) is 63% of the applied voltage (V A ) after one time constant (50 ms in this circuit). V C1 = V A x 63% = 10 x 0.63 = 6.3 Vdc In this example, the time required for the capacitor to fully charge (or discharge) is a. 250 ms. b. 50 ms. c. 99 ms. FACET by Lab-Volt 211
AC 1 Fundamentals The time constant of an RL circuit depends on the values of R and L (inductance). In the formula, equals time in seconds, R equals resistance in ohms, and L equals inductance in henries. Because pure resistance instantaneously reacts to voltage and current changes, no time constant affects a purely resistive circuit. With the aid of a universal time constant chart, you can determine the amount of voltage across or current through an inductor or capacitor if you know the time constant. The charging and discharging curves are equal and opposite. These curves indicate that a capacitor or an inductor charges and discharges at the same rate. 212 FACET by Lab-Volt
Assume that C1 is fully charged to 10 Vdc. When the switch is closed, C1 discharges through R1. The capacitor discharges at a rate dictated by the RC time constant. = R x C = 50 k x 3 F = 150 ms (one time constant) Suppose we wish to know the voltage across C1 (V C1 ) after 300 ms (two time constants). Looking at the universal time constant chart, you can see that the voltage across the capacitor will be approximately 14% of the original value after two time constants. The voltage across C1 (V C1 ) after two time constants equals: V C1 = V A x 14% = 10 x 0.14 = 1.4 Vdc FACET by Lab-Volt 213
AC 1 Fundamentals The voltage across the capacitor (C1) should be what percent of the original value (10 Vdc) after three time constants? percent (Recall Value 2) PROCEDURE If necessary clear the AC 1 FUNDAMENTALS circuit board of all two-post connectors and any other connections. Locate the RC TIME CONSTANTS circuit block, and connect the circuit shown. While monitoring the voltage across R1 (V R1 ) with an oscilloscope, press and hold (close) S1. Based on your observation, did the voltage across R1 develop instantaneously or was there a time constant delay? a. delayed b. instantaneous 214 FACET by Lab-Volt
On the RC TIME CONSTANTS circuit block, connect the circuit shown. S2 provides a discharge path for C1 through R3. Press and hold S2 for several seconds to make sure C1 is totally discharged. Connect the oscilloscope input across C1. Make sure the probe is set to 10X. Measure the time required for the capacitor to charge to V A (15 Vdc) by pressing (holding) S1 and using the second hand of a watch or clock. Begin timing at the instant you close S1. Charge time = seconds (Recall Value 1) One time constant equals the resistance times the capacitance. In your circuit: = R x C = 100 k x 10 F = 1 second Compare your measured value of total charging time ( seconds [Step 4, Recall Value 1]) to the calculated value of one time constant. Was the total time required to charge a. yes b. no FACET by Lab-Volt 215
AC 1 Fundamentals Use a two-post connector to add the 10 F capacitor C2 in parallel with the circuit. Calculate the new RC time constant of the circuit. ( = R2 x C T, C T = C1 + C2) = seconds (Recall Value 2) Use the universal time constant chart to determine the percentage of voltage across C1 and C2 (V C ) after V A is applied for two time constants. Voltage = percent (Recall Value 3) 216 FACET by Lab-Volt
Make sure the capacitors are discharged by pressing S2 (zero volts across C1 and C2). Make sure your probe is set to 10X. Determine V C after two time constants (4 seconds) have expired by pressing S1, releasing it after 4 seconds, and immediately taking the measurement. V C after 4 seconds = volts (Recall Value 4) Compare your measured voltage of V C ( volts [Step 9, Recall Value 4]) with the percentage of applied voltage across C1 and C2 by using the universal time constant chart. Can you accurately predict the voltage across a capacitor by using the universal time constant chart? a. yes b. no Do not turn off the equipment. The FACET setup is needed to answer a review question. CONCLUSION The time constant of an RC circuit equals total resistance (R) multiplied by total capacitance (C). When you know the time constant, you can use the universal time constant chart to predict the amount of charge on a capacitor at any point in its charge or discharge time. FACET by Lab-Volt 217
AC 1 Fundamentals REVIEW QUESTIONS 1. Locate the RC TIME CONSTANTS circuit block on the AC 1 Fundamentals circuit board and connect the circuit shown. Make sure the capacitor is completely discharged by pressing S2 until you measure zero volts across C1. While observing an oscilloscope connected across C1, press S1 and measure the time required for the capacitor to charge to 15 Vdc (T C ). Start timing at the instant S1 is closed. T C (without CM) = seconds (Recall Value 1) Make sure C1 is completely discharged by pressing S2 until you measure zero volts across C1. Place CM switch 3 in the ON postion to reduce the value of C1. Remeasure the time required to charge C1. T C (with CM) = seconds (Recall Value 2) You conclude that a. decreasing the capacitance increased the RC time constant. b. changing the capacitance had no effect on the RC time constant. c. decreasing the capacitance decreased the RC time constant. d. the more capacitive the circuit, the shorter the RC time constant. 2. A circuit with resistance of 75 k and capacitance of 4.7 F has an RC time constant of a. 1.59 s. b. 353 ms. c. 3.53 s. d. 159 ms. 3. Increasing the value of resistance in an RC circuit a. causes the time constant to increase. b. has no effect on the time constant. c. causes the time constant to decrease. d. 4. A capacitor is considered to be fully discharged after a. one time constant. b. six time constants. c. two time constants. d. 218 FACET by Lab-Volt
5. Use the universal time constant chart to determine a. charge and discharge times of RC and RL circuits. b. charge and discharge times of RC circuits only. c. only charge times of RC and RL circuits. d. only discharge times of RC and RL circuits. FACET by Lab-Volt 219