Section Date Alternating Current RC and LCR Circuits 37 LABORATORY 3 7 PRE-LABORATORY ASSIGNMENT 1. In a series RC circuit such as the one in Figure 37-1, the following phase relationship exists between the generator voltage V, the capacitor voltage Vc, and the resistor voltage VR. (a) V and VR are in phase, Vc lags VR by 90° (b) Vc and VR are at angle •, V leads Vc by 90° (c) Vlags Vrby 90°, Vlags VR by angle • (d) VR lags Vc by 0, Vc leads V by 90° 2. If a series RC circuit has VR=12.6 V and Vc=10.7V, the generator voltage must be (a) 12.6V (b) 23.3V (c) 1.9 V (d) 16.5 V. Show your work. 3. A series RC circuit has o=2000 rad/s and R=300 2. The voltage Vc is measured to be 4.76V, and Ve is measured to be 6.78 V. What is the value of C? Show your work. (a) 2.37 uF (b) 5.00 uF (c) 1.17 uf (d) 4.67 uF. 4. A series RC circuit of R=500 22 and C=3.00 uF is measured to have Vr=8.07 V and Vc=6.68V. What is the current I, and what is the value of o the angular frequency? Show your work. rad/s A I 0 = COPYRIGHT © 2008 Thomson Brooks/Cole 373 Physics Laboratory Manual Loyd 5. A series LCR circuit consists of an inductor of inductance L and resistancer, a capacitor C, a resistor R, and a generator of voltage V. Mark as true or false the following statements concerning the relative phase of V, V, V, Vc, and VR. 1. V, and VR are in phase. 2. Vi leads Vc by 90°. 3. V is at angle o relative to VR. 4. VL-Vc is in phase with Vr. 5. Vlags VR by 90°. 6. Measurements on the circuit described in Question 5 give VL= 10.76V, Vc=5.68V, VR=6.32V, and V.–3.75 V. What is the generator voltage V? Show your work. V V 7. An inductor with L= 150 mH and r = 2009 is in series with a capacitor, a resistor, and a generator of m=1000 rad/s. The voltage across the inductor Vind is measured to be 10.87 V, VR is measured to be 4.65 V, and Vc is measured to be 5.96 V. What is the generator voltage V? (Hint-This is the measurement to be performed in this laboratory for LCR circuits. Use the appropriate equations to find Vand V,, and then use them and the values of VR and Vc to calculate V.) Section Date LABORATORY 37 Alternating Current RC and LCR Circuits 37 LABORATORY REPORT Data Table 1 250 Hz Ck= 0-57 f= uF R (22) 300R Vc (V) hoor 3-521v 6-5361 13.558v 3.5774 0-310 3-5950 Toor 3.4551 9.Tuqu 13-5195 goor 3.386v 0.9350 / 13.5074 VR (V) V (V) Calculations Table 1 0= rad/s ſą + V % Error C (UF) uF % Error = C= uF ac= COPYRIGHT © 2008 Thomson Brooks/Cole 375 Laboratory 37 - Alternating Current RC and ICR Circuits 377 QUESTIONS 1. Comment on the agreement between the measured generator voltage V and the quantity V+V for the RC circuit data. 2. Do your results for Question 1 confirm that the capacitor has no resistance? State specifically how the data either do or do not confirm this expectation. 3. State carefully your evaluation of the precision of your measurements of the value of the capacitor in the RC circuit. State the evidence for your opinion. 4. Considering the given value of Ck as the true value, comment on the accuracy of your measurements of the capacitance. 5. Comment on the agreement between the measured generator voltage V and the quantity VV-Vc)? + (Vx+V,)? in the LCR circuit. COPYRIGHT © 2008 Thomson Brooks/Cole Physics Laboratory Manual Loyd 6. Do your results confirm the phasor diagram of Figure 37-2 as a correct model for the addition of the voltages in an LCR circuit? State why they do or do not confirm this model.
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