ليك 1.8 مة 1.6 1:4 1-2 0.8 0.6 0.4 0.2 0 -0.2 0.4 0.6 -0.0 61 Aut L graph 2 In で 917-88 Q R=47000 10-115 29 F 5 10 15 20 25 30 35 40 45 5f 60 A graph In (u) (V8) 2.0 1.6 7.4 1.2 1.1 QAI 0.8 (Inuy 0.6 0.4 0.2 0 0.2 -0.4 0.6 -8.8 10 28 ¥2 time Constat 470K 70 AT e = C= 5J 53x10 35 30 50 Gv 70 80 90 700 graph 66 2, 3 4,800 AT (S) ± 0,01 0,005 2,400 S S V +0,01 V 6, 24 1,83 5,84 1,76 5,49 1169 S 7,200 S 5,04 1,61 5 10,40 S 4,64 1,53 G 14,80 S 4,00 1,38 7 24,00 S 3,09 1,12 8. 31/60 S 2,40 0,875 q 1090 S1, 84 01604 10, 52.40 s 1136 01307 IL 83,20 01480 0,733 Note: when time is less than los (± is 0,001) AT (S) V (v) In U (v) ± 0,01 + 0,01 0,00 S 6,29 1,83 3355679 2 6,400 S 4,16 1,42 8,900 S 3,68 1,30 10,80 ما 3,12 1,13 12,90 S 2,80 1,02 19,00 S 2,56 0,940 18,00 S 2,00 0,693 24,00 S 1,36 0307 S 4 29,20 S 0, 960 10,0468 le 39/40 S 0,720 o so,980 -01328 01733 g 60 ار AT 0.6 1 .1.22 20-10 1.22 y₁ = 10 0.6 Y2 Je - Y 72-X .X2 /R 9- T T=RT == => = 20 C = R = 470000 1 -0.062 "/s 3297 7/22/ => र = 5/80 => 2² = 9 T -0.062 2 = RC " 16.1 S C h R 16.1 -5 3.42×10 = 470000 1&IC SOFT Fed Mad 20 30 3 6 v y₁ = 0.8, V₁ =37 g. = –0.4.4₂ = 74 70 80 90 100 66 graph A Ул ない 10.4-1.8 งา => 74-37 x2 Vi T R = 470000 TRC 18 10 C→F (sign) -00324 14 -1 -0.0324= 2 =) J0.0324 = 30.80 30.8 S = RC 30.8 - 47000 C 2012 470000 47000 -S C = 6.55x10 POF OPGE/n INVESTIGATION OF RC CIRCUIT BACKGROUND INFORMATION Before arriving at your lab session, you should read the background information and answer the pre-lab questions given below, in your logbook. • • Read the instructions for the practical carefully before you come, in particular the "Aims and Objectives" and "Experimental Procedure" sections. Make sure you can identify all of the equipment referred to - look these up in your notes or textbook if you are unsure of what you will need. If there are any words that you are not familiar with, look them up in a dictionary and ensure you understand what they mean. Make a note in your logbook of anything that you will need to remember. Think about the science behind the experiment. Do you understand the laws that are being investigated, and why it may be important to be able to carry out this experiment? PRE-LAB QUESTIONS After reading the background information for this experiment, complete the Pre-lab questions below in your logbook BEFORE the lab session. 1) What is the definition of the time constant in a discharging RC circuit? 2) Write down the equations for the time dependence of the voltage across the capacitor when it is discharging. 3) Sketch a discharge curve labelling key points. INTRODUCTION Capacitors are among the most-commonly used circuit elements in modern electronic devices. Your calculator and cell phone contain dozens or hundreds of them. Any two electrical conductors brought near each other form a capacitor. If a charge Q is transferred from one conductor to the other (so that one has a charge +Q and the other has charge -Q), then there will be a voltage difference V, which is proportional to the charge Q. The constant ratio Q/V is called the capacitance C. C = = The SI unit of capacitance is the farad (F). (1) A capacitor is a device which stores charge. If the two sides of a capacitor are connected across a battery of voltage Vo and then disconnected from the battery, each plate of the capacitor will carry a charge of magnitude QC V (one side has +Qo, the other has -Qo). The larger the capacitance, the larger the charge carried. If the two sides of this charged capacitor are then connected by a wire, there will be a large, brief current through the wire as the capacitor discharges. If we use a large resistance R, instead of a wire, to connect the sides of the charged capacitor, the capacitor will discharge much more slowly. The charge and the voltage on the capacitor will decrease exponentially in time, as shown in Figure1, with a time constant T = RC (T=Greek letter tau). Vo 0.37 Vo AIMS AND OBJECTIVES V τ Figure 1: Voltage vs time graph (discharging) in RC circuit ● Determine and compare the time constants (T₁ and T₂) associated with discharging stage of RC circuits. • Calculate the value of capacitance for both capacitors (C₁ and C₂). After completing the virtual experiment you must ensure you have completed the following: • A tabulated set of results, with correct units. • Identified sources of errors and stated precision of your instruments. Sketched discharging curves (exponential decay curves) of voltage vs time, labelling important features. • Plotted graphs of the corresponding In(V) vs time for the two capacitors. THEORY In this experiment, you will measure the voltage across a capacitor C that is connected in parallel to a known resistor R, by the use of a digital storage oscilloscope. By plotting graphs of voltage against time, you will be able to determine the time constant T of the circuit. This will allow you to calculate the value of the capacitor in the circuit. Consider the simple RC circuit shown below. The resistor R and capacitor C are connected to the battery Vo with switch S. Capacitor Resistor Switch Battery Figure 2: Schematic diagram of RC circuit If switch S is closed, the capacitor will be charged to a voltage Vo and will carry a charge Q₁ = C V If switch S is re-opened, a current i will flow through the resistor as the capacitor discharges. The current i, the charge q remaining on the capacitor, and the voltage v across the capacitor and resistor are related by the following equations: V = iR = Δα i =- At (2) (3) The negative sign in the second equation indicates that the charge q is getting smaller as the current i flows. Combining these two equations yields: Δα At 9 q RC τ (4) Where, we have written T = RC. Notice that T = RC has the units of time. With the initial condition q(t=0) = Q₁, the solution to this differential equation is q(t) = Qe 冷 The voltage v(t) is given by: V(t) = = (+)e (1) (1) =Ve (6) Taking the natural log of both sides of (6) yields In ln (V) τ + + In In (V) (7) (5) Hence, a plot of In(v) vs t should be a straight line with slope = -1/T PROCEDURE The circuit is assembled as shown in Figure 3 below. The circuit consists of a known resistor, R, of value 470 k with a tolerance of 5% and an unknown capacitor C. The experiment involves the charging and discharging of a capacitor. You need to first charge the capacitor. Once the capacitor is charged, investigate how the capacitor discharges by observing the trace of voltage against time on the oscilloscope. Switch 6V Battery LINI-T UTD2025C 200 Oscilloscope Po 000 Cursor Type Track Capacitor SALE VOLTSION Y Figure 3: Experimental set up of RC circuit FOBITION LEVEL CLOLD 470 ΚΩ Resistor Charging Process: ● Close the switch to charge the capacitor with V₁ = Vo. • Note that the charging process may happen quickly (almost simultaneously). Discharging Process: Open the switch and record time and the decaying voltage on the capacitor C₁ using the oscilloscope as shown in the figure 4 below. VIVEVEJU 25MMZ 250MS/s DIGITAL STORAGE OSCILLOSCOP Stop M Pos: 0.00us AT: 0.00s Vol: HZ Ta -36.00s Cursor Туре Track Tb: -36.00% Time AV. DOO a Va: 6.00V Voltage Vb: 6.00V CHI 2.00V CH2 MATH Off Off M 10.0s CH10.00mV Figure 3: Discharge curve • Record the voltage and time of 10 or more points along the exponential decay, including at least 5 or 6 points in the first part of the curve between the initial voltage V and V/3. Make sure your data points cover an appropriate range, otherwise you may not get the full curve similar to Figure1. Replace the capacitor C₁ with C₂ and repeat the above steps. LOGBOOK TASKS 1. Answer pre-lab questions. 2. Draw a fully labelled circuit diagram. 3. Sketch the discharging curves (exponential decay curve of voltage vs time) for C₁ and C2 on the same axes, labelling important features. 4. Using your data collected from the virtual experiment, plot the corresponding In(V) vs time graphs for both C₁ and C₂. a) This graph should be a straight line with slope -1/T.