Refer to the diagram. An ideal battery is connected to four resistors and one ca
ID: 1412750 • Letter: R
Question
Refer to the diagram. An ideal battery is connected to four resistors and one capacitor, with the switch initially open, as shown. Here are the known values :E,R1,R2,R3,R4,C Now the switch is closed. Find the following, expressed using only known values. a. Find the maximum charge that will be stored on the capacitor. b. Suppose the switch has been closed for a long time; now it is re-opened. Find the power being produced in R4 at the moment when the energy stored on the capacitor is at 3/4 of its maximum value. 1. Refer to the diagram. An ideal battery is connected to four resistors and switch one capacitor, with the switch initially open, as shown. Here are the known values: ,R,R,R, R,C Now the switch is closed. Find the following, expressed using R. R, only known values. a. Find the maximum charge that will be stored on the capacitor. b. Suppose the switch has been closed for a long time; now it is re-opened Find the power being produced in R, at the moment when the energy stored on the capacitor is at 3/4 of its maximum value.Explanation / Answer
A) Maximum charge on capacitor =CV where V is voltage across capacitor
= C*E*[(R2*R4)/(R2+R4)]*[R1 + {(R2*R4)/(R2+R4}]
b)Energy becomes 3/4 times when potential across capacitor becomes sqrt 3 /2 = 0.866 times
0.866 = e^-t/RC where R =R3+R4
i = io e^-t/RC
Power being produced in R4 = i^2R4
= [io *0.866]^2 *R4
= 0.75 io^2 R4
=0.75 R4*[V/(R3+R4)]^2
= 0.75 R4*[{E*[(R2*R4)/(R2+R4)]*[R1 + {(R2*R4)/(R2+R4}]}/(R3+R4)]^2