An uncharged parallel plate capacitor filled with a dielectric of dielectric constant K is connected to an air filled identical parallel capacitor charged to potential V1. If the common potential is V2, the value of K is
V1−V2V1
V1V1−V2
V2V1−V2
V1−V2V2
V1−V2V1+V2
A
V1V1−V2
B
V1−V2V1
C
V2V1−V2
D
V1−V2V2
E
V1−V2V1+V2
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Solution
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If the capacitance of the air filled capacitor is C1=C, then the capacitance of the dielectric field capacitor will be C2=KC
Now, the common potential is V2=Q1+Q2C1+C2
Here, Q1=C1V1, charge for air filled capacitor and as the dielectric filled capacitor is uncharged, Q2=0
Thus, V2=C1V1+0C1+C2
or V2=CV1C+KC
or K+1=V1/V2
or K=V1−V2V2
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