Question

two identical parallel plates capacitors c1 and c2 having capacitance c each.the space between the plates is now filled wiyhdielectric as shown.if the 2 capacitancesstill have equal capacitances.obtain the relation between the dielectric constant k1 and k2.

Answer 1

capacitance of a capacitor: C1 =$\frac{ ε0A }{(d-t)+ \frac{t}{ k_{1} } }$
C2 = $\frac{ ε0A }{(d-t)+ \frac{t}{ k_{2} } }$
C1 = C2
$\frac{ ε_{0}A }{(d-t)+ \frac{t}{ k_{1} } } = \frac{ ε_{0}A }{(d-t)+ \frac{t}{ k_{2} } }$

${(d-t)+ \frac{t}{ k_{2} } } = {(d-t)+ \frac{t}{ k_{1} } }$
k1 = k2