The R-C circuit and the time constant Review the texthook on RC Circuits: Phys 1

Question

The R-C circuit and the time constant Review the texthook on RC Circuits: Phys 1402: Serway/Vuille: Section. 18.5, Active Figure 18.17, Quick Quiz 18.9 Phys 2426: Serway/Jewett: Section 28.4, Active Figure 28.16, Quick Quiz 28.5 1. In Figure I, with the capacitor originally uncharged, the recording starts (t-0) at the moment the switch is closed by connecting to A. What is the voltage across the capacitor at t-0? What is the voltage across the capacitor at t =oo? Why? (VO)-0 because there is no charge on the capacitor, V(o)- 1.2V because the capacitor is fally charged) 2. The switch in Figure 1 is flipped from point A to point B disconnecting the battery and the capacitor starts discharging. During the process of the discharge, is there a current flowing through the Resistor? What direction (leftward or rightward)? (Yes, there is a current flowing through the Resistor to the right) 3. During the process of the discharge, is there a current flowing through the Capacitor? (No, there is no current through the Capacitor) 4. In Figure 1, the capacitance of the capacitor is 5.0uF and the resistance of the resistor is 3.50M what is the time constant for this circuit? (17.5s) 5. In Figure 1, the capacitance of the capacitor is 5.00F and the resistance of the resistor is 3.50 MC2. How long would it take to charge the capacitor up from zero to 63% of the battery voltage? Close to one time constant = 17.5s) 6. If the resistance of the resistor from Figure 1 is adjusted from 3.50M22 to a smaller value, how would it affect the time constant? Would the capacitor charge faster or slower? (It will lower the time constant; the capacitor will charge faster) 7. If the capacitance of the capacitor from Figure I is adjusted from 50uC to a larger value, how would it affecet the time constant? Would the capacitor charge faster or slower? (It will increase the time constant, the capacitor will charge slower) Figure 1. RC Circuit

Explanation / Answer

1) At t = 0 , there is no current flow in the circuit due to open switch. Therefore, V = 0. Now when we close the switch, the current starts flowing and at t = (infinity) , V = 1.2 V

2) Yes, current will obviously flow through the resistor

3) during discharge, no current flows through the capacitor,

4) Equation for time constant T is given as

T = R*C where R is resistance and C is capacitance

T = 5E-6*3.5E+6

T = 17.5 SECONDS

5) It will take about 17 seconds that is close to one time constant.

6) As we can see time constant is directly proportional to resistance, so lowering the resistance will make the capacitor charge faster.

7) It will increase as time constant is directly related to capacitance and thus it will charge slowly.

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