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 = 11.0 V, C = 5.10 mu F, and R = 7.60 times 10^5 ohm, find the following. (a) the time constant of the circuit s (b) the maximum charge on the capacitor mu C (c) the charge on the capacitor after 6.10 s Your response differs from the correct answer by more than 100%. mu C (d) the potential difference across the resistor after 6.10 s Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. V (e) the current in the resistor at that time A Use the values from PRACTICE IT to help you work this exercise. (a) Find the charge on the capacitor after 2.20 s have elapsed. Q = C (b) Find the magnitude of the potential difference across the capacitor after 2.20 s. Delta V_C = V (c) Find the magnitude of the potential difference across the resistor at that same time. Delta V_R = V

Explanation / Answer

PRACTICE IT:

(a) T = R C = (7.60 x 10^5)(5.10 x 10^-6)

= 3.88 s

(b) Maximum charge = C e = (5.10 uF)(11 V)

= 56.1 uC

(c) Qc = Qo [1 - e^(-t/T)]

Qc = 56.1 [ 1 - e^(-6.10 / 3.88)]

Qc = 44.45 uC

(d) Vc = Qc / C = 44.45 / 5.10 = 8.72 Volt

V_R = 11 - 8.72 = 2.28 Volt

(e) I = V_R / R = 2.28 / (7.60 x 10^5) = 3 x 10^-6 A

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EXERCISE:

(a) Q = 56.1 [ 1 - e^(-2.20 / 3.88)] = 24.3 uC

(b) Vc = Q / C = 24.3 / 5.10 = 4.76 Volt

(c) VR = 11 - 4.76 = 6.24 Volt

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