A circuit is made with the components capacitor resistor...

A circuit is made with the components: capacitor, resistor, battery and switch, all in series. The battery potential is 18 volts. With the switch in the open position, the capacitor is discharged. Then at time t = 0, the switch is closed, and the potential difference across the capacitor is noted. It is seen that 1 s after the switch is closed, the capacitor attains a potential difference of 5 volts. What is the time constant for this circuit? Write your answer in seconds.

Transcript

00:01 Hi there, so for this problem, we are told that an rc circuit initially uncharged has a 60 -bolts battery connected to a capacitor with a capacitance that is given, that is 200 micropharets, and a resistor of 50 oms.

00:19 If the switch s1 is then closed at the time equals to zero, while keeping the switch to open, we need to calculate the following.

00:33 So for part a of this problem, we need to calculate the time constant of the circuit.

00:40 Now, the time constant of the circuit is just simply the product between the resistance and the capacitance.

00:47 So we just simply substitute those values in here.

00:50 The resistance is 50 oms, and the capacitance is 200 micro.

00:58 That means 10 to the minus 6 ferrets.

01:03 So from this, we obtain that the time constant of this circuit is equal to 0 .0 seconds.

01:16 So that's a solution for part a of this problem.

01:19 Now for part b, we are asked about the charge at the 5 milliseconds.

01:31 So we are given the time of 5 milliseconds that is the same as 5 times 10 to the minus 3 seconds.

01:40 And we need to determine the charge in the capacitor for that time.

01:46 Now, we know that for an rc circuit in the process of charging, and we will have that the charge is equal to the product between the capacitance and the voltage, and that times one minus the exponential of minus the time, divided by the, time constant.

02:23 So with that said, we just need to simply substitute the values to determine the charge after 5 milliseconds.

02:30 So that will be the capacitance that is 200 times 10 to the minus 6 farrats that times the potential difference or the battery that we are given that is 60 balls that times one minus the exponential of minus the times the that is 5 times 10 to the minus 3 seconds divided by the time constant that is 0 .01 seconds.

03:06 So from this we obtain a charge of 4 .72 times 10 to the minus 3 columns.

03:22 So we can also write that as 4 .72 millicoloms...

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