Question

Two identical sized capacitors C1 and C2 are connected with a battery as shown in figure. Capacitor plates are square plates. A dielectric slab of dielectric constant K=2, are filled in half the region of the two capacitors are shown:

C→ capacity, q→ charge stored, U→ energy stored.

Match the following two columns

C→ capacity, q→ charge stored, U→ energy stored.

Match the following two columns

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Solution

Capacitance of air filled parallel plate capacitor is C0=Aϵ0d where A= area of plate and d= separation between plates.

Here C1 contains two capacitor of area A/2 and separation d. They are in parallel.

Thus, C1=(A/2)Kϵ0d+(A/2)ϵ0d=(A/2)2ϵ0d+(A/2)ϵ0d=C0+C0/2=32C0

As C2 is filled half by dielectric slab so C2=Aϵ0d−d/2+d/2K=Aϵ0d/2+d/22=43Aϵ0d=43C0

∴C1C2=(3/2)C0(4/3)C0=98 thus A→3

As C1 and C2 are in series so charges on both are same.

∴q1q2=1 thus B→1

Energy U=q22C, As q is same for both so U∝1C

∴U1U2=C2C1=89

Thus C→2

Here C1 contains two capacitor of area A/2 and separation d. They are in parallel.

Thus, C1=(A/2)Kϵ0d+(A/2)ϵ0d=(A/2)2ϵ0d+(A/2)ϵ0d=C0+C0/2=32C0

As C2 is filled half by dielectric slab so C2=Aϵ0d−d/2+d/2K=Aϵ0d/2+d/22=43Aϵ0d=43C0

∴C1C2=(3/2)C0(4/3)C0=98 thus A→3

As C1 and C2 are in series so charges on both are same.

∴q1q2=1 thus B→1

Energy U=q22C, As q is same for both so U∝1C

∴U1U2=C2C1=89

Thus C→2

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