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Question
A capacitor stores 50 µC charge when connected across a battery. When the gap between the plates is filled with a dielectric, a charge of 100 µC flows through the battery. Find the dielectric constant of the material inserted.
Solution
Given:
Initial charge on the capacitor = 50 µC
Now, let the dielectric constant of the material inserted be k.
As 100 µC of extra charge flows through the battery, the net charge on the capacitor becomes
50 + 100 = 150 µC
Now ,
`C_1 = q_1/V = (∈_0A)/d` ............(i)
`C_2 = q_2/V = (∈_0Ak)/d` ............(ii)
On dividing (i) by (ii), we get
`C_1/C_2 = q_1/q_2 = 1/k`
⇒ `50/150 = 1/k`
⇒ `k = 3`
Thus, the dielectric constant of the given material is 3.
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