Question

8. Capacitance in circuits, RC circuits When a voltage source Vo is applied to a capacitor in a circuit which has a resistance R, a charge Q CV will build up across the capacitor. This does not happen instantaneously, but takes some time. The charge builds up exponentially with a characteristic time r = RC. Charging: V = v. 1 - e-t/RC) Discharging: Vc = V e-t/RC Page 2 of 3 When t = RC , the exponential is lle, or 0.37. In this part of the experiment you will build a RC circuit, and measure the characteristic time ERC. Choose a large value of both capacitance and resistance so that the characteristic time is about 40 seconds or higher. (The values shown in the circuit diagram are some typical value; you may use any other values as convenient). Set the potentiometer to give 1.0 V. You will be using the large PASCO capacitors so be aware of the polarity of the capacitor. Connect the multimeter to measure the voltage across the capacitor. Use a DPDT (double pole double throw) switch, so that one can easily switch between configurations of charging the Capacitor to one of discharging. Charge the Capacitor to 1.0 Volt. You will see that the voltage across the capacitor builds up immediately for the above circuit (since the resistor is not in the circuit while charging). When you flip the switch to the discharge position the capacitor will discharge slowly through the resistor. Once you feel comfortable with the operations you can take data to measure the time constant R 100 KO 330 F BAT 1.5 V SW

Answer 1

as V = Voet/re log on both sides Taking logo lub Into the Rc. So I will plot int is t and Alipe will give RC which is I. 'T Slabe lur t Eq. of line we V. 0.89.9 10.813 0.732 0.663 10.596 0.54 0:49 -- 0.10 G -0.201 --- 0 312 -0,411 --01511 got in gooph. IMV 0.02% -0-0152 e Jo IS 20 26 30 35 40 45 -0.616 ㅗ 0.02 RC TERC-1 0.02 0.441 0.397 -0.113 -0.819 |-0.924 -1.02 -1-02 S5 z=50 02362 0.327 0.296 0-267 0.242 -1.22. This is time constant. 65 0.218 0:19.8 0.179 0.163 0,141 0.134 0.121 -|-32 -1.42 -152 -1-62 -1.72 -1.81 -1.92 -2.00 hill To TS 8o 85 90 95 100 los Mo 0.019 -231 115

-0.4- M P -0.9 - Y-Dependent -1.4- -1.9 - -2.41 0 20 40 60 80 100 120 X - Independent Regression Line (j = -0.023 - 0.02) Calculation Summary Sum of X = 1380 Sum of Y = -27.945 Mean X= 60 Mean Y = -1.215 Sum of squares (SSx) = 25300 Sum of products (SP) = -505.9 Regression Equation = = bx + a b= SPISSx= -505.9/25300 = -0.02 a = My - bMx = -1.22 - (-0.02*60) = -0.01524 ŷ = -0.02X -0.01524