Questions 18-20 Consider a parallel plate capacitor of capacitance Co connected
ID: 776491 • Letter: Q
Question
Questions 18-20 Consider a parallel plate capacitor of capacitance Co connected to a battery of voltage Vo. The distance between the plates is d and each plate is a square of side L. A dielectric material of dielectric constant K is inserted a distance r between the parallel plates of the capacitor is shown in the figure. 18. Which of the following is the capacitance as a function of x? (a) Co (1f(Kt 1)E) (e) Co(+-1) (b) CO (1 + KE) (c) Co(14(K-)E) (d) Co (1 + (2x-1)) 19. Assuming that the potential difference between the plates is kept constant (by keeping the voltage source in the system), which of the following is the energy stored in the capacitor after the dielectric is inserted? (Uo is the stored energy before the dielectric material is inserted.) (a) to (1 + (K-1) (b) UO (1 + (K + 1)t) (d) U0 (1 + (2x-1)) (c) Uo(1 + (K-2)) 20. Assuming that the charge on the capacitor is kept constant (by removing the battery after charging the plates and before the (e) Us(1 + Kt) dielectric is inserted), which of the following is the energy stored in the capacitor after the dielectric is inserted? (Vo is the stored energy before the dielectric material is inserted.) 1+(-2)EExplanation / Answer
when dielectric is not inserted.
Co = A*epsilon/d
= L^2*epsilon/d
Here the capacitor can be tretated as two capacitors connected in series.
C1 = k*(x*L)epsilon/d
= k*x*Co/L
C2 = L(L-x)*epsilon/d
= (L-x)*Co/L
Ceq = C1*C2
= (k*x*Co/L)*((L-x)*Co/L)/(k*x*Co/L + (L-x)*Co/L )
= Co*(1 + (k-1)*x/L)
18) c) Co*(1 + (k-1)*x/L)
19) a) Uo*(1 + (k-1)*x/L)
20) c) Uo/(1 + (k-1)*x/L)
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