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Question

# Two identical sized capacitors C1 and C2 are connected to a battery in series. A dielectric slab of dielectric constant K=2 is filled in the half region of both the capacitors as shown in figure. (C→ capacitance, q→ charge stored, U→ energy stored ) Match the following column: Column I Column II (A) C1C2 (p) 8/9 (q) 4/9 (r) 9/8 (s) None of these (B) q1q2 (C) U1U2

A
Ar, Bp, Cs
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B
Ar, Bs, Cp
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C
As, Bs, Cs
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D
Ap, Br, Cq
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Solution

## The correct option is B A→r, B→s, C→pLet original capacitance of capacitor without dielectric is C0=Aϵ0d In C1, capacitor is in parallel combination. So equivalent capacitance will be C1=ϵ0(A/2)d+Kϵ0(A/2)d ⇒C1=Aϵ02d+Aϵ0d (∵K=2) ⇒C1=C02+C0=3C02 Similarly, for the second capacitor, C2=Aϵ0d−t+tK ⇒C2=Aϵ0d−d2+d2×2 (∵t=d2; K=2) ⇒C2=2ϵ0Ad(1+12)=43Aϵ0d ∴C2=43C0 Hence, C1C2=98 Since capacitors are in series, ∴q1=q2 ⇒q1q2=1 And we know that energy stored in a capacitor is given by U=q22C ∴U1U2=C2C1 (because q is same for both) Thus, U1U2=4C0/33C0/2=89 Hence, A→r, B→s, C→p

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