9:36 AM Thu Mar 7 Ll RC Circuit.pdf Lab Instructions V0.0 January 29, 2018 A Simple RC Circuit Objective To study the charging and discharging of a capacitor and to determine the time constant of a simple RC circuit. Overview In this experiment you will set up a simple RC circuit, and obtain a graph of the voltage AVe across a capacitor versus time, first, while it charges and then, while it discharges. From each of these graphs you will determine the time constant 7 of the circuit. Figure 1: Left: Charging circuit. Right: Discharging circuit The circuit diagram on the left in Figure 1 shows a RC circuit with resistor R, capacitor C' and a voltage source with emf &, all connected in series. Let the capacitor be initially discharged, so that at t = 0, AV = 0. At t = 0, the switch is closed and the capacitor begins to charge. Application of K LL leads to the following differential equation for AV during charging (Phys 121 students, ignore differential equations 1 and 3, and proceed to Equations 2 and 4), dAVe & AVe i d RC RC' & The above equation, with the initial condition AVy = 0, can be solved to give, For use by the physics department, Ohlone College, Fremont, CA. ! 5 Calendar Ii' To Do D Notifications |\\__/| 151073 9:36 AM Thu Mar 7 Ll RC Circuit.pdf Lab Instructions V0.0 January 29, 2018 AVc(t) = (1 e"7c), (2) which describes AV as a function of during the charging of the capacitor. In the circuit diagram on the right in Figure 1, the voltage source is disconnected and when the switch is closed at = 0 and the capacitor starts discharging through the resistor. This time, application of K LL leads to the following differential equation for AVy during discharging, dAVe Alg (3) dt RC The above equation, with the initial condition AVy = &, can be solved to give, i AVe(t) = &e e (4) which describes AV as a function of during the discharging of the capacitor. The time constant 7 = RC', determines how slow or fast the charging/discharging happens. Figure 2 shows plots of Equation 2 and Equation 4. Figure 2: Left: Charging curve. Right: Discharging curve In this experiment vou will obtain the charging and discharging plots like those in Figure 2. Note that the maximum voltage that can be safely applied across R is given by A'/vlllfl.l' = V P\"!HJ,'R' (5) where P4, is the maximum rated power dissipation inside the resistor, and is printed on the bag containing the resistor. Since, the maximum voltage across R in this experiment will be &, you must ensure that &