Online-Lab-4_Capacitors

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Electrical Engineering

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Apr 3, 2024

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PHYS 1402 Lab 4: Capacitors Name: ___Andrea Zaragoza ____ Objectives  To discover how the capacitance of conducting parallel plates is related to the area of the plates and their separation. Overview Any pair of conductors that can be charged electrically so that one conductor has excess positive charge and the other conductor has an equal amount of excess negative charge on it is called a capacitor. Capacitors are widely used in electronic circuits where it is important to store charge and/or energy or to trigger a timed electrical event. For example, circuits with capacitors are designed to do such diverse things as setting the flashing rate of Christmas lights, selecting what station a radio picks up, and storing the electrical energy needed to fire an electronic flash unit. The easiest type of capacitor to analyze is the parallel-plate capacitor. We will focus exclusively on studying the properties of parallel-plate capacitors as they are easy to construct, and their behavior can be predicted using simple mathematical calculations and basic physical reasoning. We will focus on studying capacitors in DC (direct current) circuits. The circuit symbol for a capacitor is simply a pair of parallel lines. Circuit symbols of battery and capacitor are shown in figure 1. Figure 1 The usual method for transferring equal and opposite charges to the plates of a capacitor is to use a battery or power-supply to produce a potential difference between the two conductors. Electrons will then flow from one conductor to the other until the potential difference produced between the two conductors is equal to that of the battery. In general, the amount of charge needed to produce a potential difference equal to that of the battery will depend on the size, shape, and location of the conductors relative to each other as well as the properties of the material between the conductors. The capacitance of a given capacitor is defined as the ratio of the magnitude of the net or excess charge Q on either one of the conductors to the voltage V applied across the two conductors. 1

C = Q V For a fixed voltage from a battery, the net charge found on either plate is proportional to the capacitance of the pair of conductors and the applied voltage Q = CV In the next activity, you can begin exploring capacitance between parallel plates. You will be using PhET simulation Capacitors (https://phet.colorado.edu/sims/html/capacitor-lab-basics/latest/capacitor-lab-basics_en.html ) Click on “Capacitance” and run simulation. Familiarize yourself with the simulation. Play around with the settings, change the battery voltage, the distance between the plates of the capacitor and area of the capacitor plate. When you are finished testing all the settings, click on the “Reset All” button. Step 1: Let’s find out how the capacitance depends on the area of the capacitor plates. Keeping the separation fixed, increase the area of the plates by dragging the green double arrow near the edge of the top plate. Notice how the capacitance changes as you increase the area, notice how it changes when you decrease the area. Question 1: Does the capacitance increase or decrease as the area of the plates increases? The capacitance increases. Step 2: Set the separation “d” between the plates to 2 mm (or 0.002 m since 1 m = 1000 mm) by dragging the green double arrow symbol above the upper plate of the capacitor. Plate area by default is 100 mm 2 (or 100 x 10 -6 m 2 ), do not change it. Step 3: Check the box labeled as “Capacitance”. The capacitance of the capacitor is now displayed. Step 4: Keeping the area fixed A = 100 x 10 -6 m 2 , change the separation between the plates and record the new capacitance along with the new distance. 2

Question 2: What mathematical relationship best describes the dependence of capacitance on plate separation? The capacitance of a parallel-plate capacitor is inversely proportional to the distance between the plates So far, we have only looked at the capacitance of a capacitor, it depends on the geometrical shape of the capacitor (area and separation of capacitor plates). It is independent of the battery voltage that is used to charge the capacitor. Step 5: Let’s charge the capacitor now. Adjust the separation to 10 mm and the area of the plates to 400 mm 2 . Adjust the battery voltage to 1.5 V using the sliding bar on the battery. Check the boxes “Capacitance”, “Top Plate Charge”, and “Stored Energy”. Touch the leads of the battery to the plates of the capacitor. Step 6: Keeping the battery voltage at 1.5 V, slowly decrease the battery voltage and observe how the capacitance, stored energy, and the charge on the capacitor change. Question 3: Does the charge increase or decrease as the battery voltage decreases? As the battery decreases, the charge will decrease as well. Question 4: Does the capacitance increase or decrease as the battery voltage decreases? It would remain the same. Question 5: Does the stored energy increase or decrease as the battery voltage decreases? The stored energy decreases. Step 7: Keeping the battery voltage at 1.5 V, slowly decrease the separation between the plates and observe how the capacitance, stored energy, and the charge on the capacitor change. Question 6: How does the capacitance, stored energy, and charge on the capacitor increase or decrease as the separation decreases? In this condition, the voltage is constant, and the separation of plates decreases, then the Capacitance increases because it is indirectly dependent on distance. C ∝ 1d Charge is increasing because it is directly dependent on capacitance. Q ∝ C The stored energy is increasing because it is directly dependent on capacitance. E ∝ C Step 8: Charge the plates of the capacitor. Next disconnect the battery. Now slowly decrease the separation between the plates and observe how the capacitance, stored energy, and the charge on the capacitor change. Question 7: How does the capacitance, stored energy, and charge on the capacitor increase or decrease as the separation decreases? Because the battery is detached, the capacitor always has a charge. Distance is getting shorter, which causes the capacitance to increase. Because capacitance is an indirect 3

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dependency on stored energy in this scenario, the stored energy is diminishing. Because capacitance is indirectly dependent upon itself, the voltage on the capacitor is dropping . Question 8: Does the voltage between the plates increase or decrease as the separation decreases? Step 9: Charge the plates of the capacitor. Next disconnect the battery and leave the plates fully separated at 10 mm. Now slowly decrease the area of the plates and observe how the capacitance, stored energy, and the charge on the capacitor change. Question 9: How does the capacitance, stored energy, and voltage between the plates increase or decrease as the plate area decreases? Capacitance decreases when the plate area decreases because C ∝ A The voltage on the capacitor is increasing when the capacitance decreases because V ∝ 1/C The stored energy is increasing when the capacitance is decreasing because E ∝ 1/C 4

Online-Lab-4_Capacitors

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