An air filled parallel plate capacitor charged to potential \(V_1\) is connected to uncharged parallel plate capacitor having dielectric constant \(k\). The common potential of both is \(V_2\). What is the value of \(k\)?
\(\frac{V_1 - V_2}{V_1 + V_2}\)
\(\frac{V_1 - V_2}{V_1}\)
\(\frac{V_1 - V_2}{V_2}\)
\(\frac{V_1}{V_1 - V_2}\)
Solution:
Using conservation of charge, the initial charge is \(Q = C V_1\). When connected in parallel to an uncharged capacitor of capacitance \(kC\), the total capacitance becomes \(C(1+k)\). Thus, \(C V_1 = C(1+k)V_2 implies k = \frac{V_1-V_2}{V_2}\).
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