Question

If a capacitor is filled with n dielectric slabs of thickness t1, t2…….. tn, then this arrangement is equivalent to n capacitors in series. Find out the expression of net capacitance.

Answer 1

I hope this  helps. .....

Answer 2

The expression of net capacitance for the capacitor filled with n dielectric slabs of thickness t1, t2…….. tn, is Ceq = kεA/(t₁+t₂+t₃+......tₙ).

Given:

A capacitor is filled with n dielectric slabs of thickness t1, t2…….. tn.

To Find:

The expression of net capacitance.

Solution:

We are required to find the expression of net capacitance for the capacitor filled with n dielectric slabs of thickness t1, t2…….. tn.

We know that the dielectric slabs are connected in series inside the capacitors.

So, the net capacitance can be given as

1/Ceq = 1/C₁+1/C₂+1/C₃+............1/Cₙ --------(1)

We know the formula for capacitance, C = kεA/t in equation(1) where k is constant for n dielectric slab and area A remains the same in series.

1/Ceq = t₁/kεA+ t₂/kεA+t₃/kεA+..........+tₙ/kεA.

1/Ceq = 1/kεA (t₁+t₂+t₃+......tₙ)

Ceq = kεA/(t₁+t₂+t₃+......tₙ)

Therefore, The expression of net capacitance for the capacitor filled with n dielectric slabs of thickness t1, t2…….. tn, is Ceq = kεA/(t₁+t₂+t₃+......tₙ).

#SPJ3