A fully charged capacitor has a capacitance 'C'. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity 's' and mass 'm'. If the temperature of the block is raised by 'DeltaT', the potential difference 'V' across the capacitance is

Options

A. `sqrt((2mC Delta T)/(s))`
B. `(mC Delta T)/(s)`
C. `(ms Delta T)/(C )`
D. `sqrt((2ms Delta T)/( C))`

Answer

D

Explanation

`E = ((1)/(2))CV^(2)` The energy stored in capacitor is lost in form of heat energy. `H = ms Delta T`
`:. Ms Delta T = ((1)/(2)) CV^(2), C = (q_(1) + q_(2))/(V_(A) - V_(B)) = (q_(1) + q_(2))/((q_(2))/(C_(2)) + (q_(1))/(C_(1)))`
`:. C = (2C_(1) C_(2) + C_(3) (C_(1) + C_(2)))/(C_(1) + C_(2) + 2C_(3))`
`:. V = sqrt((2m s Delta T)/(C ))`