EE40 Guide P1 Lab 4 Lab Experiment Guide for RC Circuits I Introduction 1 Capacitors A capacitor is a passive electronic component that stores energy in the form of an electrostatic field The unit of capacitance is the farad coulomb volt Practical capacitor values usually lie in the picofarad 1 pF 10 12 F to microfarad 1 F 10 6 F range Recall that a current is a flow of charges When current flows into one plate of a capacitor the charges don t pass through although to maintain local charge balance an equal number of the same polarity charges leave the other plate of the device but instead accumulate on that plate increasing the voltage across the capacitor The voltage V across the capacitor capacitance C is directly proportional to the charge Q stored on the plates Q CV Since Q is the integration of current over time we can write v t Q t i t dt C C Differentiating this equation we obtain the I V characteristic equation for a capacitor i t C dV t dt Eq 1 2 RC Circuits An RC resistor capacitor circuit will have an exponential voltage response of the form t v t A Be RC where constant A is the final voltage and constant B is the difference between the initial and the final voltages e x is e to the x power where e 2 718 the base of the natural logarithm The product RC is called the time constant whose units are seconds and is usually represented by the Greek letter When the time has reached a value equal to the time constant then the voltage is Be RC Be l 0 368 B volts away from the final value A or about 5 8 of the way from the initial value A B to the final value A The characteristic exponential decay associated with an RC circuit is important to understand because complicated circuits can oftentimes be modeled simply as resistor and a capacitor This is especially true in integrated circuits ICs A simple RC circuit is drawn in Figure 1 with currents and voltages defined as shown Equation 2 is obtained from Kirchhoff s Voltage Law which states that the algebraic sum of voltage drops around a closed loop is zero Equation 1 above is the defining I V characteristic EE40 Guide P2 Lab 4 Lab equation for a capacitor and Equation 3 is the defining I V characteristic equation for a resistor Ohm s Law Vin VC VR VR IR RC dVC dt Eq 2 Eq 3 Combining Equations 1 and 3 into 2 we obtain the following first order linear differential equation dV Eq 4 Vin VC RC C dt If VIN is a step function at time t 0 then VC and VR are of the form VC A Be t RC VR A B e Eq 5 t RC If a voltage difference exists across the resistor i e VR 0 or VR 0 then current will flow Eq 3 This current flows through the capacitor and causes VC to change Eq 1 VC will increase if I 0 or decrease if I 0 exponentially with time until it reaches the value of VIN at which time the current goes to zero since VR 0 For the square wave function VIN as shown in Figure 2 a the responses VC and VR are shown in Figure 2 b and Figure 2 c respectively EE40 Guide P3 Lab 4 Lab Note that if the frequency of the square wave VIN is too high i e if f 1 RC then VC and VR will not have enough time to reach their asymptotic values If the frequency is too low i e if f 1 RC the decay time will be very short relative to the period of the waveform and thus the exponential decay will be difficult to observe As a rough guideline the period of the square wave should be chosen such that it is approximately equal to 10RC in order for the responses shown in Figure 2b c to be readily observed on an oscilloscope 3 Inductors An inductor is a passive electronic device that stores energy in a magnetic field The unit of inductance is the henry volt second ampere Practical values of inductance range from one microhenry 1 H 1 x 10 6 H to one henry 1 H Inductors are usually made by highly coiled wires in which changing current generate a magnetic field By Lenz s Law the changing magnetic flux produces a back EMF electromotive force or a potential in the opposite direction of current flow and magnetic flux While capacitors act to oppose changes in voltage inductors oppose changes in current The voltage v t across an inductor with inductance L is equal to the inductance multiplied by the change in current di t dt through the inductor di t v t L Eq 6 dt II Hands On 1 Determining the RC Circuit Configuration In this part of the experiment you will make ohmmeter measurements to see if you can discover a method to determine if a resistor and capacitor are connected in series or in parallel EE40 Guide P4 Lab 4 Lab Get a 5 1 k resistor and 100 F capacitor from your TA Recall that an ohmmeter has a built in current source that sends a small current into the circuit under test The ohmmeter reads the voltage across the circuit under test and determines the resistance of the circuit using Ohm s Law Build the circuit shown in Figure 3 Note that the ohmmeter s current source keeps on charging up the capacitor For small values of capacitance the capacitor will be fully charged almost instantly Question 1 Are you able to measure the value of the resistor If not explain the reason why you cannot make the measurement Build the circuit shown in Figure 4 Note that the capacitor stops charging when the current through the resistor is equal to the current from the ohmmeter Question 2 Explain how you got your ohmmeter reading for the circuit in Figure 4 Why does it take some time before the ohmmeter s reading stabilizes Question 3 Given a black box with either a series or parallel RC circuit can you determine the RC configuration using an ohmmeter If so how Identifying Physical Values in a Series RC Circuit Black Box and a Parallel RC Circuit Black Box The TA will give you two black boxes if available One contains a series RC circuit and the other contains a parallel RC circuit Determine the basic resistorcapacitor configuration in each black box using an ohmmeter If you are instructed to build the black box yourself note that you are not allowed access to the node shared by RB and CB so you can t measure RB directly Please use the breadboard Question 4 Determine whether each block box is a series or parallel RC circuit 2 Series RC Circuit Black Box Construct the circuit below for the black box that contains the unknown resistor RB and capacitor CB in series There is an …
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