Two identical condensers M and N are connected in series with a battery. The space between the plates of M is completely filled with a dielectric medium of dielectric constant 8 and a copper plate of thickness d2 is introduced between the plates of N (d is the distance between the plates). Then potential differences across M and N are, respectively, in the ratio:
1:6
1:4
4:1
3:8
A
4:1
B
1:4
C
1:6
D
3:8
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Solution
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Let the capacitance of the condenser M be C and N be C′.
The new capacitance of the condenser M will be, CM=εCM=8C
When a copper plate of thickness d/2 is inserted in between the capacitor N, effective distance between plates reduces to d−d/2=d/2.
Since, C∝1d,C′=2C
Since, the two condensers are connected in series, charge one each capacitor is same.
⇒VM:VN=1CM:1CN=18C:12C
⇒VM:VN=1:4
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