Please give the reasoning behind them A parallel plate capacitor with plate sepa

Question

Please give the reasoning behind them

A parallel plate capacitor with plate separation d is connected to a battery. The capacitor is fully charged to Volts. (C is the capacitance and U is the stored energy.) Select true or false for each statement. Coulombs and a voltage of V to the battery, decreasing d increases C. With the capacitor connected to the battery, decreasing d increases U True With the capacitor connected False | False·After being disconnected from the battery, inserting a dielectric with x > 1 will increase U. False·After being disconnected from the battery, increasing d decreases V False With the capacitor connected to the battery, decreasing d decreases Q. True After being disconnected from the battery, decreasing d increases C. Submit Answer Incorrect.Tries 2/6Previous Tries

Explanation / Answer

we know that the capacitor is device used to store the charge and electrical energy

the relations are as follows Q = C*V

and capacitance of a capacitor is C = epsilon_0*A/d

with dielectric material of constant k , the capacitance increases by a factor of k that is t

the capacitance with dielectric material is C' = k*C

c is capacitance without dielectric material.

the energy stored is U = 0.5*C*V^2 = Q^2/2C = Q*V/2

so

with battery , decreasing d increases C --TRUE

with battry connected to capacitor,decreasing d increases U --- Fasle

disconnected from battery, and with dielectric material k>1 , U inreases ---- True

disconnected from battery , increasing d, decreases v --- False

concected to battery ,decreasing d , decreases Q -- False,

Q = C*V = epsilon_0*A/d*V, as the battery is connected the potential is same so q*d = constant that means the charge and distance are inversly proportional to each other

connected with battery, decreasing d increases C --- False

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