CapacitanceHard
Question
A parallel plate capacitor without any dielectric has capacitance C0. A dielectric slab is made up of two dielectric slabs of dielectric constants K and 2K and is of same dimensions as that of capacitor plates and both the parts are of equal dimensions arranged serially as shown. If this dielectric slab is introduced (dielectric K enters first) in between the plates at constant speed, then variation of capacitance with time will be best represented by:
Options
A.
B.
C.
D.
Solution
Case − I When dielectric slab of dielectric constant K enters in to the capacitor.
At any time t, there will be two capacitors are in parallel combination - one with air and other with dielectric slab.
C(t) = Cair + Cslab
=
=
[ L − (K − 1) Vt] (linear function of t)
Its slope = M C(t) =
(K − 1) V
Case − II When dielectric slab of dielectric constant 2K also enters into the capacitor.
C′ (t) = Cslab 1 + Cslab 2
=
=
[L + Vt] (linear function of t)
Its slope = MC′ (t) =
As = M C′ (t) > MC (t)
and both C(t) and C′(t) are linear function of ′t′ hence variation of capacitance with time be best represented by (B)
At any time t, there will be two capacitors are in parallel combination - one with air and other with dielectric slab.
C(t) = Cair + Cslab
=
=
[ L − (K − 1) Vt] (linear function of t)Its slope = M C(t) =
(K − 1) VCase − II When dielectric slab of dielectric constant 2K also enters into the capacitor.
C′ (t) = Cslab 1 + Cslab 2
=
=
[L + Vt] (linear function of t)Its slope = MC′ (t) =
As = M C′ (t) > MC (t)
and both C(t) and C′(t) are linear function of ′t′ hence variation of capacitance with time be best represented by (B)
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