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A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 38 , R3 = 61 and R4 = 150 . The capacitance is C = 48 F and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign.
What is Q(), the charge on the capacitor after the switch has been closed for a very long time?
After the switch has been closed for a very long time, it is then opened. What is Q(topen), the charge on the capacitor at a time topen = 680 s after the switch was opened?
What is IC,max(closed), the current that flows through the capacitor whose magnitude is maximum during the time when the switch is closed? A positive value for the current is defined to be in the direction of the arrow shown.
Explanation / Answer
Q(), the charge on the capacitor after the switch has been closed for a very long time
Voltage across capacitor = 12/(38 + 61 +150) * 61
= 2.94 V
=> Q(), the charge on the capacitor = 48 *10-6 * 2.94
= 1.41 *10-4 C
the charge on the capacitor at a time topen = 680 s = 1.41 *10-4 * e(-0.1431)
= 1.22 *10-4 C
IC,max(closed), the current that flows through the capacitor whose magnitude is maximum during the time when the switch is closed
=> IC,max(closed) = 0.05676 *61 /38
= 0.0911 A
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