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Last updated 9/18/07 Lab 4: DC Capacitors Lab Format: Cookbook/Quantitative Concepts • Capacitance, Voltage, and Charge • Series and Parallel configurations of Capacitors Objectives • Verify equivalent capacitance formula for parallel and series conbination. Materials • • • • 1F capacitor (reference capacitance) 3 1F capacitors to make parallel and series Power Supply (set it to 2 V output) Cables and jumper wires Introduction We know from class that the charge (Q) stored in a capacitor is determined by its capacitance (C) and the voltage across it (V): Q = CV Equation 1 We also know that when a voltage is applied to a capacitor, charge flows in one side and exits the other side, hence the charge on the positive side is equal in magnitude and opposite in sign to the charge on the negative side: V +Q -Q We can measure the capacitance of a capacitor indirectly if we connect it in series with a known capacitor, see diagram below (Vo=Power supply) +Q -Q Vo C1 (known) +Q C2 (unknown) -Q 1 By measuring the voltage (V1) across the known capacitor, you can deduce Q (Q=C1V1). The key concept is that the same amount Q is stored in the unknown capacitor (why?). Now if you measure the voltage (V2) across the unknown capacitor, you can find C2 in terms of C1. Work out the relationship. If you use a “common” voltmeter to measure the voltage across the capacitor (say C1) you may see the voltage reading decreases from a finite value to zero. The basic problem is that a voltmeter has a finite resistance (not infinite), it draws a current and discharges the capacitor that you want to measure. It turns out that the time it takes to discharge is proportional the product of the capacitance (C) and resistance (R) of the voltmeter. It is called the RC time constant (we will cover that in class next week). In our case, we have chosen a very large capacitance (1 Farad) and a voltmeter with large internal resistance very ~ 106 ohms, hence the time it takes to discharge is ~ RC~106 seconds. So, you shouldn’t have any problem taking the voltmeter reading. Using this procedure for measuring capacitance, you will proceed to verify the equivalent capacitance of parallel and series combinations. Procedure 1) Use one 1F capacitor as the reference capacitance or known capacitor. Connect two 1F capacitors in a parallel combination as treat this as an unknown capacitor, see diagram below. +Q -Q Vo C1 (known) +Q C2 (unknown) -Q Note: Important! (A) These 1 F capacitor has a polarity, that is, a positive lead and a negative lead. You must have the positive lead of the capacitor connect to the positive lead of the power supply. Let the TA inspect your circuit before turn on the power supply. (Always turn off the power supply when you manipulate the circuit) (B)The maximum voltage for these capacitors are 2.5V. Set your power supply to no more than 2V just to be safe not to damage the capacitors. Now “Measure” (determine) the equivalent capacitance C2 using the method outlined in the introduction. Although these capacitors are labeled as 1 F, their values are uncertain with ± 5%. When you check your measured equivalent ! 2 capacitance vs. the theoretical formula, use error analysis to determine the uncertainty in your measured equivalent capacitance and see if it agrees with theoretical value. Questions: Is V2 greater or less than V1? Is C2 greater or less than C1? How much charge is stored in each of capacitor in the parallel combination? 2) Simialr to procedure (1) but disconnect the two 1uF capacitors in a parallel combination and re-connect them in a series combination. Also answer the questions: Is V2 greater or less than V1? Is C2 greater or less than C1? What are the charges and voltage for each of capacitor in the series combination? 3) Now take 3 1F capacitors and connect then in a series-parallel combination, see diagram below. +Q -Q Vo C1 (known) +Q C2 (unknown) -Q “Measure” the equivalent capacitance C2 using the method outlined in the introduction. Q. Is V2 greater or less than V1? Is C2 greater or less than C1? What are the charges and voltage for each of capacitor in this series-parallel combination? 4) If you have time left. Ask the TA for some 1µF (10-6 Farad) capacitors and redo procedure 1. What happens to the voltmeter reading? What is the RC time constant? 3