When two charged
conductors
connected there
would be
loss
of
energy
Why ? prove it.
Answers
Explanation:
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Explanation:
Redistribution of Charges and Loss of Energy by Combination of Charged Conductors Two charged conductors which have different potential are combined and then charges on them get.
Redistributed and the potential become same on both of it. In this process, a definite energy is lost. Redistribution of Charges From figure, two isolated conductors A and B are of radii R1 and R2 respectively and the capacitances are C1 and C2 respectively. On charging A by Q1 and B by Q2 , their potentials become V1 and V2 respectively. Before joining the conducting wire, Q1 = C1V1 …………. (1) and Q2 = C2V2 ……………… (2) Thus, total amount of charge on both the conductors, Q = Q1 + Q2 or, Q = C1V1 + C2V2 …………… (3) Now, if both the conductors are attached by a conducting wire of negligible resistance or capacitance.
Then charge always flow the conductor of high potential to low potential and flows till the potential on both the conductors is same. In electrical equilibrium, let the potential be V and charges on the conductors be Q’1 and Q’2 respectively. Then, total capacitance on arrangement of the two conductors as a system, C = C1 + C2 because the potential on both the conductors is same and hence the conductors are in parallel combination. After redistribution of charges, Q’1 = C1V ………………. (4) and Q’2 = C2V ……………. (5) Then, total charge after redistribution, Q = Q’1 + Q’2 = (C1 + C2) V From law of conservation of charge, C1V1 + C2V2 = (C1 + C2)V Thus, common potential,
Thus, after redistribution of charges, the ratio of charges of conductors,
After redistribution of charges, the ratio of charges of conductors is in the ratio of their capacitances. If V1 > V2 Then, V1 > V > V2 Change in potential of first conductor,
In the redistribution process of charges, the charge flows through the conducting wire. Hence, some amount of energy is changed in the form of heat and some amount of energy is lost. It is due to the resistance of conducting wire. Total potential energy of the system before joining conducting wire,
