A parallel-plate capacitor with plates of area LW and plate separation has the r

Question

A parallel-plate capacitor with plates of area LW and plate separation has the region between its plates willed with wedges of two dielectric materials as shown below. Assume is much less than both L and W, (a) determine its capacitance. (b) Should the capacitance the same if the labels ki and kzare interchanged? Demonstrate that your expression does or does not have this property. (c) Show that if ks and k approach equality to a common value k, your result becomes the same as the capacitance of a capacitor containing a single dielectric: C-ksolW/t

Explanation / Answer

Solution) Dielectrics in parallel

Ceq=C1+C2

C1=K1(epsilon not)(LW/2)/t

C2=K2(epsilon not)(LW/2)/t

Ceq=(1/2)(K1+K2)((epsilon not)(LW)/t

(b) Even if K1 and K2 are interchanged the equivalent capacitance value do not change as discussed above .

So it remains the same .

(c) if K1=K2=K

Ceq=(1/2)(K1+K2)((epsilon not)(LW)/t

Ceq=(1/2)(2K)(epsilon not)(LW)/t

Ceq=K(epsilon not)(LW)/t

Hence proved .

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