Physics 248, Spring 2009 Lab 7: Capacitors and RC-Decay

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1 Name Section Physics 248, Spring 2009 Lab 7: Capacitors and RC-Decay Your TA will use this sheet to score your lab. It is to be turned in at the end of lab. To receive full credit you must use complete sentences and explain your reasoning clearly. In this lab, you will study the properties of capacitors by completing two related investigations: (1) the variation of the potential difference with the plate separation for a parallel plate capacitor, and (2) measurements of the voltage across capacitors in series and in parallel, and the discharging of a capacitor through a resistor in an RC circuit. Experiment 1, EC-3, Part 1. In this experiment, you will measure the potential difference across the capacitor plates as a function of the plate separation. The procedure is given in the lab manual for lab EC-3, Part I, Experiment A. You should skip the preliminary questions (Q1.1 and Q1.2). Follow steps 1-3. Do not do Experiment B. Several points of clarification: 1. Note that you will take data manually in this experiment rather than using the PASCO box and the computer interface. 2. Keep in mind that the power supply is only used to charge the capacitor initially; it is not connected permanently in the circuit as in Figure 1a (otherwise Q would not be fixed). To charge the capacitor, you simply touch the lead of the DC power supply to the fixed plate. 3. If the weather is especially dry or humid, the charge on the capacitor plates can be affected. Directions in the manual are provided which can help minimize any effects due to weather conditions, if needed (consult your TA). In step 3, you are asked to plot voltage V vs. plate separation d. (Do not bother to fit the data to the model function as indicated in the manual.) Place your plot in the space given on the next page.

2 Indicate the places in your plot where there is a deviation from the behavior of an ideal capacitor (Q1.3). What do you think the reasons might be for this deviation? (Q1.4, part 1). Please enter your answers below. You may skip the rest of Q1.4, as well as questions Q1.5 and Q1.6, and go on to Experiment 2. 2

3 Experiment 2. EC-3, Part II. This experiment consists of two parts. In Experiments A and B, you will measure the potential difference across capacitors in series and in parallel. In Experiment C, you will observe the time dependence of the potential difference across a capacitor that is discharging through a resistor. EC-3, Experiment IIA: Capacitors in series. Follow the procedure given in the lab manual. Summarize your results for the predicted and measured potential difference across each capacitor in the table below. Predicted ΔV Measured ΔV C 1 C 2 EC-3, Experiment IIB: Capacitors in parallel. Once again, follow the procedure in the online lab manual. Summarize your results for the predicted and measured potential difference across the parallel combination in the table below. Predicted ΔV Measured ΔV C! 3

4 EC-3, Experiment IIC, Capacitor discharging through a resistor. In this experiment, you will study the discharge of a charged capacitor through a resistor in a closed circuit (circuits with capacitors and resistors are known as RC circuits). Until now, you have only studied the steady state behavior of capacitors, in which the charge and voltage are related by Q = CV. However, when a capacitor is charged by a battery or is discharged through a resistor, there is a transient behavior in which the charge on the plates and voltage across the capacitor are time-dependent, such that Q(t) = CV(t). The flow of charge is called the current, I = dq(t) dt. (Note that I is defined with an overall minus sign in the lab manual. This sign will not concern us here.) In the charging of a capacitor, the capacitor is connected to a battery and a resistor R, a device that hinders the flow of charge. Current flows through the circuit until there is an appropriate charge buildup on the capacitor plates. In the discharging of a capacitor, the battery is removed from the circuit, and charge flows from one plate to the other, draining the capacitor of its charge. Once the charge on the capacitor has been fully depleted, the current in the circuit falls to zero. Here we will study only the discharging of the capacitor. You will measure the voltage across the capacitor as a function of time, and see that it (and therefore also the charge) follows an exponential decay law: V(t) = V 0 e!t ", in which V 0 is the initial voltage, and! is known as the time constant of the circuit. The time constant is related to the values of R and C by! = RC. The units of R are! (ohms), which are! = V (C " s #1 ). (You should verify that RC has units of time). Follow the procedure in the lab manual for Experiment C. Please be sure the PASCO box is turned on before turning on the computer, otherwise the computer will not recognize the PASCO box and you will need to restart. You will do the experiment for two values of the resistance. Print (or write) out a copy of your data for each case and present the results in the space provided on the next page (or the last page if needed). 4

5 Directly from the data on the computer, for each case measure the time constant! of the circuit by determining the time when the voltage has dropped to 1 e of its initial value. Next, calculate! from the resistor and capacitor values, and compare it to your experimentally obtained result. List your results in the table below. (Q2.2; skip Q2.1.) R (!) C (F) Measured! (s) R! C (s) 5

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