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 (?)

 

[asteriatic]

.

There are a few factors that could impact the capacitance in a circuit when a thin sheet of aluminum is added.

Firstly, the distance between the plates of the capacitor will decrease when the thin sheet of aluminum is added, as it takes up some of the space between the plates. This would typically result in an increase in capacitance, as the distance between the plates is a key factor in the capacitance formula.

However, the aluminum sheet itself may also have a dielectric strength, which could impact the overall capacitance. If the dielectric strength of the aluminum is high, it could act as a better insulator, increasing the capacitance. On the other hand, if the dielectric strength is low, it could act as a conductor and decrease the capacitance.

Additionally, the shape and size of the aluminum sheet could also play a role in the overall capacitance. A larger sheet may have a bigger impact on the overall capacitance than a smaller one, and a sheet with a different shape could also affect the distribution of electric field lines, resulting in a change in capacitance.

Overall, the addition of a thin sheet of aluminum in a circuit could potentially increase or decrease the capacitance, depending on various factors such as distance, dielectric strength, and shape. Therefore, the correct answer is (d) May increase or decrease.