Space between the plates of a parallel plate capacitor of plate area 4cm2 and separation of (d) 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is ______ pF. (Given ε0=8.85×10−12F/m)
Answer: 15
Solution
The two slabs, each of thickness 2d, stack one above the other and so behave as two capacitors in series. The slab with K=5 gives C1=d/25ε0A=20pF and the slab with K=3 gives C2=d/23ε0A=12pF, taking A=4×10−4m2 and 2d=0.885×10−3m. In series these give 20+1220×12=7.5pF, and adding the 7.5pF capacitor in parallel yields 7.5+7.5. The effective capacitance of the combination is 15pF.
