An uncharged capacitor and a resistor are connected in series to a source of emf

Question

An uncharged capacitor and a resistor are connected in series to a source of emf. If = 6.00 V, = 22.0 F, and R = 100 , find the following (a) the time constant of the circuit ms (b) the maximum charge on the capacitor (c) the charge on the capacitor at a time equal to one time constant after the battery is connected 63.2 Your response differs from the correct answer by more than 10%. Double check your calculations. C Need Help? Read It +2/3 points | Previous Answers SerPSET9 28.P.038 Consider a series RC circuit as in the figure below for which R = 9.00 MQ, C = 1.00 , and = 27.0 V (a) Find the time constant of the circuit 9 (b) What is the maximum charge on the capacitor after the switch is thrown closed? 27 HC (c) Find the current in the resistor 10.0 s after the switch is closed 136.2 what mathematical function describes the time dependence of the current in an RC circuit? A

Explanation / Answer

Q1) given = 6 V , C = 22*10^-6 F , R = 100 ohms

The time constant of the circuit

t = R* C

= 100 * 22 x 10-6 F

= 0.0022s

= 2.2 ms

b) The maximum charge on the capacitor

qo = CVo

= 22 x 10-6 F * 6 V

= 132 C

c) The charge on the capacitor after one time constantis

           q= qo (1 - e-t/RC )

At, t = 1 RC ,

q= qo (1 - e-1 )

= 132 C * (1 - 0.368 )

= 83.424*10^-6 C

= 83.424 C

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