Question

An uncharged capacitor and a resistor are connected in series to a source of EMF. If ε = 6.63 V, C = 21.1 μF, and R = 122 Ω, calculate the time constant τ of the circuit.

Answer 1

Isn't the time constant for resistor capacitor circuits:
\[\tau = RC\]
Where you need to be consistent with your units.
If you have ohms you need to use Farads.
If you have microFarads you need to use megaOhms.

Answer 2

I am still a little confused

Answer 3

\[1ohm = \frac{ kg \times m^2 }{ s^3 \times A^2 }\]
\[1 Farad = \frac{ s^4 \times A^2 }{ m^2 \times kg }\]

Answer 4

If you multiply them together your units will all disappear except for Seconds.

Answer 5

You currently have microfarads and ohms. You either need to change convert to just Farads which would be easier or to megaOhms so that you are consistent.

Answer 6

so now converted to 2.11E-5 and 122.06

Answer 7

You only need to convert 1

Answer 8

and I just multiply them together?

Answer 9

You need to have Ohms times Farads or microFarads times megaOhms.

Answer 10

You currently have microFarads and Ohms.

Answer 11

okay so I converted 21.1 to 2.11E-5 F
then I times that by the 122ohms?

Answer 12

Okay I got that to be 2.57ms which is right, now would you know how to find the max charge?

Answer 13

"find the maximum charge on the capacitor"

Answer 14

nvm I figured that out lol. But last one

Answer 15

Calculate the charge on the capacitor after one time constant.

Answer 16

I don't recall the formulas so I have to look them up but glad its getting easier now.
\[Q = CV_b(1-e^{-\frac{ t }{ RC }})\]
Where Vb represents the voltage of the battery

Answer 17

Thank you!!

Answer 18

My pleasure