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Question

Two identical capacitors are connected as shown in the figure. A dielectric slab is introduced between the plates of one of the capacitors so as to fill the gap, the battery remaining connected. The charge on each capacitor will be :(charge on each condenser is q0; k = dielectric constant )


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A
2q01+1/k
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B
q01+1/k
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C
2q01+k
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D
q01+k
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Solution

The correct option is A 2q01+1/k
When capacitors are connected in series the charge present on them must be equal.
Qc1+Qc2=2 ------------ (1)
Now when k is introduced c2 becomes kc2

Let qo be the charge on capacitor
given c1=c2
2qoc=2,qoc=1 from (1)
c=qo

After introducing the dielectric, let charge on each plate become Q1
Q1qo+Q1kq0=2
kQ1+Q1kqo=2
Q1=2kqok+1
Q1=2qo1+1k

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