How does a thin sheet of aluminum impact capacitance in a circuit?

[aimiit]

Homework Statement

As shown in the figure, a very thin sheet of aluminium in placed in between the plates of the condenser. Then the capacity
(a) Will increase (b) Will decrease (c) Remains unchanged (d) May increase or decreas

Homework Equations

Dielectric strength of a metal.

The Attempt at a Solution

Since dielectric constant for a metal is infinty, and the formula for capacitance is :
ε_oA/ d - t + \frac{t}{k}
If k = infinity, and t/k = t/infinity = 0.

Then we will be left with ε_oA/ d - t

Since denominator is decreasing, the value of C should increase. Therefore my answer is (a) Will increase.
But the correct answer is (d) May increase or decrease

 

[cupid.callin]

Look it at like this, plates of capacitor are metallic (generally) and you also introduced a metallic plate,

So you can assume 2 sides of introduced plate as two individual plates connected with a wire. So you get 2 series capacitors ...

 

[aimiit]

How would that help?

 

[cupid.callin]

That way you can find net capacitance and then compare the new and prevoius capacitances.

PS: forgot to mention this before, you can assume plate area as A and distance as d
New plate are after inserting plate will be (?) and the distance between plates of 2 new formed capacitors will be (?)