Question

A parallel-plate capacitor with plates of area lw and plate separation h has the region between its plates filled with wedges of two dielectric materials as shown below. Assumet is much less than both and w Let us consider a strip of width dx and length w at position x from the front left corner. We can approximate this capacitor as equivalent to two capacitors in series. 1) Find the capacitance of the upper part C1 can be expressed in terms of ki, E. w. h. l. x, and de it) Find the capacitance of the lower part C can be expressed in terms of kz, 60, while X, and doc. il) Find the equivalent capacitance of the whole slice Casce in terms of K1, K2, 80, whilex, and dr. Find the total capacitance or łhe capacitor Ciobar, using met bdx = In} ax + bl.

Answer 1

,

Capauteen leof the upper past =a= toki w dac Ci toki wdr - to kiwl dx ħ clase) hah 6 da pi > C2 = Capacitance of lower bart to Kz wodrae Sec - न 10 = toka woda toka hooldx ha I feeno = hh = 1 teen - as y = ha aid 1 2 squivalent rapacitance of the whole slice = (slice Calire ecre2 - ок, loud or slire - citla hldase) oko Log оl se hoc to welda ( k g + K 2 ) to ki ke wilde y h(x)(1-10) (d-x) kpet. K2/1-20) to K1 K2 voldoe 1 1 - h (kist ka fil-x)) Total capacitance of the capacitor = (total = Seslice to ki ka lol - I kad + (k1-12) - ki ko's Topkg -(Er-v2_) 1) ki-k2 -to kl 12 Wol Sale In (A) hki-127 in (A)