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Q.

An uncharged parallel plate capacitor having a dielectric of dielectric constant K is connected to a similar air cored parallel plate capacitor charged to a potential V₀. The two share the charge, and the common potential becomes V. The dielectric constant K is

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a

$\frac{V_{0}}{V} - 1$

b

$\frac{V_{0}}{V} + 1$

c

$\frac{V}{V_{0}} - 1$

d

$\frac{V}{V_{0}} + 1$

answer is A.

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Detailed Solution

$C_{1} = C, V_{1} = V_{0}, C_{2} = KC, V_{2} = 0, and V_{common} = V$

We know that

$V_{common} = \frac{C_{1} V_{1} + C_{2} V_{2}}{C_{1} + C_{2}}$

$∴ V = \frac{{CV}_{0} + KC \times O}{C + KC}$

or $K = \frac{V_{0}}{V} - 1$

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An uncharged parallel plate capacitor having a dielectric of dielectric constant K is connected to a similar air cored parallel plate capacitor charged to a potential V0. The two share the charge, and the common potential becomes V. The dielectric constant K is