Discussion
Two air core capacitors of equal capacitance C are connected in series. If one of them is filled with a dielectric substance of dielectric constant k, the effective capacitance becomes
Answer: B
The effective capacitance is \(\frac{kC}{1 + k}\).
Filling one capacitor with the dielectric raises its capacitance to \(kC\). The two are in series:
\[ \begin{aligned} \frac{1}{C_{eff}} &= \frac{1}{C} + \frac{1}{kC} = \frac{k + 1}{kC} \\ C_{eff} &= \frac{kC}{1 + k} \end{aligned} \]
Check: with \(k = 1\) (no dielectric) this gives \(\frac{C}{2}\), the usual result for two equal capacitors in series. The option \((k + 1)C\) is the parallel combination, and \(\frac{2kC}{1 + k}\) is double the correct value.
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