When and then connected to a battery, the total stored energyis 7.4 times greater than when they are connected in series andthen connected to the same battery. What is the ratio of the two capacitances?(Before the battery is connected in each case, the capacitors arefully discharged.) (C1)/(C2)= When and then connected to a battery, the total stored energyis 7.4 times greater than when they are connected in series andthen connected to the same battery. What is the ratio of the two capacitances?(Before the battery is connected in each case, the capacitors arefully discharged.) What is the ratio of the two capacitances?(Before the battery is connected in each case, the capacitors arefully discharged.) (C1)/(C2)=
Explanation / Answer
from problem ( 1/ 2) C V^2 + ( 1/ 2) C ' V ^ 2 = 7.4 ( 1/ 2) [ CC' / (C+C' ) ] V ^ 2 C + C ' = 7.4 CC' / ( C + C ' ) ( C + C ' ) ^ 2 = 7.4 CC' ----( 1) C + C ' = 2.72 CC' ---(2) ( C-C' ) ^ 2 = ( C + C ' ) ^ 2-4CC' = 7.4 CC' - 4C C ' Since from eq ( 1) = 3.4 CC' C-C ' = 1.8439CC' -----( 3) eq( 1) + eq ( 2) ==> 2C = 4.563CC' 4C^2 = 20.82 (CC' ) 4 C = 20.82 C ' C / C ' = 5.207