The right side has part A and part B questions. Consider the two awes shown belo

Question

The right side has part A and part B questions. Consider the two awes shown below. In Case One two identical capacitors are connected to a battery with emf V. In Case Two, a di-electric slab with dielectric constant K fills the gap of capacitor C2. Let C be the resultant capacitance for Case One and C? the resultant capacitance for Case Two. The ratio V2?/V1 of potential differences across capacitor C2 for the two cases is The ratio U?/U of total energy stored in the capacitors for the two cases is

Explanation / Answer

C1 = C2 = x

C = C1*C2/(C1+C2) = x/2

Q = C*V = C1*C2*V/(C1+C2)

V2 = Q/C2 = C1*V/(C1+C2) = v/2

U = 0.5*C*V^2

case 2

C' = (C1*k*C2)/(C1+kC2) = kx/(1+k)

Q' = C'*V = ((C1*k*C2*V)/(C1+kC2)

V2' = Q2'/kC2 = (C1*V)/(C1+kC2)) = v/(1+k)

U' = 0.5*C'*v^2

V2'/V2 = (C1+C2)/(C1+kC2)

C1 = C2

V2'/V2 = 2/(1+k)

option 5   <-------------answer

--------------------

U'/U = C'/C

U'/U = kx/(1+k)/(x/2)

U'/U = 2k/(k+1)

option 2   <-------------answer

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