Question

You have a 3000 ohm resistor, a 10 mF capacitor, and a 100V battery. Assume the battery is ideal and that the capacitor is initially uncharged. You connect the battery, resistor, and capacitor in series and complete the circuit, forming a loop. A) How much time passes before the capacitor reaches 2/3 of its maximum charge? B) What is the magnitude of the current when the capacitor is at 2/3 maximum charge? C) How much charge is on the capacitor 10 seconds after the capacitor reaches 2/3 maximum charge?

Answer 1

Solution! Resistance, RS 3000 ohm Capacitance, C = 10mF 210-9 X10 F Bartery Voltage, E = 100 Volt When capacitor is charging [1- e-t/CR 9- 3 90 9.90 Now, eje 90-911- e-t/CR ) -t/CR e t/cR = 1.0986 110986 x 10x109 x Booo 32.958 s. Therefore, time passes 32.958 S. B) The charging Current is ¿=¿e e-HICR E/CR Ź E R е. 32.058 10x10^9 x 3000) e 100 3000 1 1 1 mA. c) Now, charge t'lch - e CE LI- on the capacitor after los -> 90 [!- (Here, t'a (32.058 +10) (42.958)/10 x 10 x 3000 = 42.0585) -1.43 10 x 10 9 x 8100 100 [ 0.76c -e 9' e 1