Use the worked example above to help you solve this problem. An uncharged capaci

Question

Use the worked example above to help you solve this problem. An uncharged capacitor and a resistor are connected in series to a battery, as shown in the figure above. If epsilon = 14.0 V, C = 5.50 meuF, and R =- 7.90 x 105 omega, find the following. the time constant of the circuit the maximum charge on the capacitor the charge on the capacitor after 6.40 s the potential difference across the resistor after 6.40 s the current In the resistor at that time Use the values from PRACTICE IT to help you work this exercise. Find the charge on the capacitor after 1.80 6 have elapsed. Find the magnitude of the potential difference across the capacitor after l.80 s. Find the magnitude of the potential difference across the resistor at that same time.

Explanation / Answer

A.

time constant: t = RC = 4.345 s

B.

maximum charge: Qmax = CVmax = 77 uC

C.

Charge on the capacitor: Q = C[V0(1 - e-t/RC)]

                                            = 59.348 uC
D.

Potential difference:

           dV = V-[V0(1 - e-t/RC)] = 3.2 V

E.

Current I = dV/R

---------------------------

a.

Charge: Q = Qmax [ 1 - e-t/RC]

here, Qmax = CVmax

b.

potential difference: V = V0 [ 1 - e-t/RC], here, V0 = e = 1 4V

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