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Transcript
Book Reference : Pages 100-101 1. To look at how capacitor discharge may be examined in the lab 2. To revisit capacitor applications (particularly timing circuits) 3. To understand charging a capacitor through a fixed resistor When measuring the voltage across the resistor during discharge one can use a oscilloscope, multimeter, or data logger as long as it has a very high resistance to reduce the current flow through it Charge Discharge Switch V0 C Fixed resistor R OR OR Either way we plot a graph of the results to establish the time constant “RC”. Data loggers are ideal for this application and simplify the process As an example of using capacitor discharge as a timing mechanism consider a burglar alarm which has a delay between being trigged and sounding the siren Switch Charge Discharge V R C The bell electronics will ring the bell if the voltage across the capacitor drops below a predetermined level once it has been trigged by changing the switch location. The delay can be selected by choosing the size of R and C (as in the time constant RC) Charging a capacitor through a fixed resistor is similar to discharging (in the opposite sense) Switch 1. When the switch is closed, initially a significant current flows C V0 Fixed resistor R 2. As the capacitor charges, the pd across it increases and the current flow reduces 3. Once fully charged the pd across the capacitor is equal to V0 and current no longer flows As the voltage increases the charge increases in the same manner (from Q = CV) In this case the time constant RC is at 0.63 Q0/V0 (0.37 more to reach Q0/V0) Charge (Q) and pd (V) graphs have exactly the same shape The current graph is gradient of the charge graph (since I=Q/t) & hence decreases exponentially Since it is a series circuit, at any given time during charging.... V0 = resistor pd + capacitor pd This can be expanded as V0 = IR + Q/C Assuming initially the capacitor has no charge then the initial current I0 is I0 = V0 / R and at any given time : I = I0 e–t/RC An uncharged 4.7F capacitor is charged to a pd of 12V through a 200 resistor and then discharged through a 200k. Calculate : The initial charging current [60mA] The energy stored in the capacitor at 12V [0.34mJ] The time taken for the pd across the capacitor to fall from 12v to 3v [1.4s] The energy lost by the capacitor in this time [0.32mJ] A 68F capacitor is charged by connecting it to a 9V battery & then discharging it through a 20k resistor. Calculate : The initial charge stored [0.61C] The initial discharge current [0.45mA] The pd and the discharge current 5s after the start of the discharge [0.23V, 11A] A 2.2F capacitor is charged to a pd of 6V & then discharging it through a 100k resistor. Calculate : The charge & energy stored at a pd of 6V [13C, 40J] The pd across the capacitor 0.5s after discharge started [0.62V] The energy stored at this time [0.42J]