In the circuit shown in Fig. E26.51, C = 5.90 , ε= 28.0 V, and the emf has negligible resistance

In the circuit shown in Fig. E26.51, C = 5.90 , ε= 28.0 V,...

In the circuit shown in $\textbf{Fig. E26.51}$, $C =$ 5.90 $\mu$F, $\varepsilon =$ 28.0 V, and the emf has negligible resistance. Initially the capacitor is uncharged and the switch $S$ is in position 1. The switch is then moved to position 2, so that the capacitor begins to charge. (a) What will be the charge on the capacitor a long time after S is moved to position 2? (b) After $S$ has been in position 2 for 3.00 ms, the charge on the capacitor is measured to be 110 $\mu$C. What is the value of the resistance $R$? (c) How long after $S$ is moved to position 2 will the charge on the capacitor be equal to 99.0% of the final value found in part (a)?

Transcript

00:01 Okay, so in this question, the switch can be positioned in place 1 and 2.

00:09 In place 2, in position 2, the capacitor gets charged, right? so the question is asking us in part a, what will be charged in the capacitor a long time after s is moved to position 2? now, after a long time, after a long time, the capacitor will be able to position 2.

00:33 Fully charged that is q0 and this will be equal to a capacitance times the emf of the battery or the source so this is equal to 5 point c is given e is given right c is 5 .9 into 10 to the power minus 6 fyrite in si so plug this value of c and e you get q0 to be 165 microcunuch all right so this is this would be the charge on the capacitor after a long time so let's move on to part b after the s is position in this position to for time t equals to three milliseconds then the charge on the capacity is measured okay after three seconds the charge was measured to be 110 micro columns so the question is asking what is the resistance are all right so for that we can use the exponential equation for the charging of capacitor that is q is equal to q not times one minus e to the power minus t by rc all right now the question says that q equal to 110 and q not is 165 we don't need to convert micro column into column because they both cancel out on lhs and rhs.

02:11 So 1 minus e to the power minus now t is 3 into the power minus 3 upon r is what we need to determine and c is given as 5 .9 into the power minus 6.

02:29 Now the left is just mathematics to solve r from this equation.

02:34 This gives us that r equals to 462 .8 omens.

02:45 So we also calculated the resistance r...

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