In given circuit, \( C_1 = C_2 = C_3 = C \) initially. Now, a dielectric slab of dielectric constant \( K = \frac{3}{2} \) is inserted in \( C_2 \). The equivalent capacitance becomes
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The insertion of a dielectric increases the capacitance by a factor equal to the dielectric constant.
Step 1: Understanding the Effect of Dielectric.
When a dielectric slab of dielectric constant \( K \) is inserted into a capacitor, the capacitance increases by a factor of \( K \). Thus, for the capacitor \( C_2 \), its new capacitance becomes \( K C \), while \( C_1 \) and \( C_3 \) remain the same. Step 2: Finding the Total Capacitance.
The equivalent capacitance is found using the formula for capacitors in series and parallel:
\[
\text{Total Capacitance} = \frac{1}{\frac{1}{C_1} + \frac{1}{C_2'} + \frac{1}{C_3}}
\]
where \( C_2' = K C \). Substituting and simplifying gives:
\[
\text{Total Capacitance} = \frac{5C}{7}.
\]
Step 3: Conclusion.
The correct answer is (A), \( \frac{5C}{7} \).
