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Question

Two identical capacitors 1 and 2 are connected in series to a battery as shown in figure. Capacitor 2 contains a dielectric slab of dielectric constant k as shown. Q1 and Q2 are the charges stored in the capacitors. Now the dielectric slab is removed and the corresponding charges are Q′1 and Q′2.
Then
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A
Q1Q1=k+1k
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B
Q2Q2=k+12
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C
Q2Q2=k+12k
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D
Q1Q1=k2
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Solution

The correct option is B Q2Q2=k+12k
The capacitor 1 has capacitance C and as dielectric contains in capacitor 2 so its capacitance becomes kC.
The net capacitance Ceq=C.kCC+kC=Ck1+k
and Qeq=CeqE
When dielectric is reemoved from capacitor 2, its capacitance becomes C.
now net capacitance Ceq=C.CC+C=C2
and Qeq=CeqE=CE2
When the capacitors are connected in series, they each have the same charge as the net capacitance. Thus, Qeq=Q1=Q2 and Qeq=Q1=Q2
Q1Q1=Q2Q2=2kk+1

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