Two identical parallel-plate capacitors have a capacitance of 20 uF. When a die
ID: 2227258 • Letter: T
Question
Two identical parallel-plate capacitors have a capacitance of 20 uF. When a dielectric is inserted into one of?the capacitors, completely filling the space between the plates, its capacitance increases to 80 uF. The 80uF capacitor and the 20-uF capacitor are connected in parallel and charged to a potential di fference of 180 V. The voltage source is then disconnected. a) What is the stored energy of this system, in Joules? b) What is the charge on each capacitor, in Coulombs? The dielectric is now removed from the 80-uF capacitor. c) What is the new charge on each capacitor, in Coulombs? d) What is the fi nal stored energy of this system, in Joules?Explanation / Answer
when a dielectric let 'K' is inserted between the plates of capacitors then the capacity is increased by K times. here, 20uF has changed to 80uF so the value of K is 4. K=4. when capacitor C1 and C2 are connected in parallel then the total capacity of the system is C1+C2. the total capacitance is 20+80=100uF. a) since they are conneted across 180V the total charge on the system is Q=CV. Q=180 *100 Q=18000C. the energy stored is 1/2CV^2=1/2 *100*180*180 =1620000 joules.(actually no need to calculate the total charge). b)the total charge will distribte accordind to there capacities so divide in 80:20=4:1 ratio. implies charge on 20uF capacitor is 3600 C and on 80uF is 14400 C. c) since the system is disconnected from battery and dielectric is removed no charge will loss. so both the capacitor will have equal capacity so, charge on each capacitor is 9000 C. d)since there is a rearrangement of charges some energy might have loss.for that u calculate the present energy of the system. E=Q^2/2C==9000*9000/2*20=2025000 J. for two capacitor =2025000*2=4050000J.. THIS IS THE ASKED PROBLEM BUT I WILL GIVE U SOME CONCEPT FOR SOLVIND OTHER PROBLEMS when the battery is disconnected whatever happens to the system the total charge on the system is constant. and when it is connected obiously the voltage across is constant.
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