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InterviewSolution
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A glass plate totally fills up the gap between the electrodes of a prallel-plate capacitor whose capacitance in the absence of that glass plate is equal to `C = 20 nF`. The capacitor is connected that glass voltage source `V = 100 V`. The plate is slowly, and without friction, extracted from the gap. Find teh capacitor energy increment and the mechanical work perfomed in the process of plate extraction. |
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Answer» Initailly, capacitance of the system `= C epsilon` So, initial energy of the system : `U_(i) = (1)/(2) (C epsilon) V^(2)` and finally, energy of the capacitor : `U_(f) = (1)/(2) C V^(2)` Hence capacitance energy increment, `Delta U = (1)/(2) CV^(2) - (1)/(2) (C epsilon) V^(2) = - (1)/(2) CV^(2) (epsilon - 1) = 0.5 mJ` From enerfgy conservation `Delta U = A_("cell") + A_("agent")` (as there is no heat liberation) But `A_(cell) = (C_(f) - C_(i)) V^(2) = (C - C epsilon)V^(2)` Hence `A_("agent") = Delta U - A_(cell)` `= (1)/(2) C (1 - epsilon) V^(2) = 0.5 m J` |
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