Question

(A) Equivalent capacitance is lower than the least of capacitors present in series.
(B) One method of increasing the capacitance is to decrease the distance between plates and increase cross-sectional area.
(C) Electric field inside an isolated capacitor decreases after inserting a dielectric.
(D) Displacement of charge does not happen when a dielectric is inserted in an isolated capacitor because dielectric acts like an insulator.
(E) Energy of an isolated capacitor increases when a dielectric is inserted in the capacitor.
Of the following statements, which are true?

• A. A, B, D
• B. C, D
• C. A, B, C, D
• D. A, B, C, E

Hint:

Always check whether the capacitor is {isolated} or {connected to a battery} — energy behavior changes completely in these two cases.

Answer 1

The Correct Option is C

Concept:
Capacitance and energy of a capacitor depend on geometry, dielectric medium, and whether the capacitor is isolated or connected to a source. Statement-wise Analysis:
(A)
{Equivalent capacitance is lower than the least of capacitors present in series.} In series combination: \[ \frac{1}{C_{\text{eq}}} = \sum \frac{1}{C_i} \] Hence, \(C_{\text{eq}}\) is always less than the smallest capacitor. \(\Rightarrow\) True
(B)
{One method of increasing the capacitance is to decrease the distance between plates and increase cross-sectional area.} Capacitance: \[ C = \varepsilon_0 \varepsilon_r \frac{A}{d} \] Decreasing \(d\) and increasing \(A\) increases \(C\). \(\Rightarrow\) True
(C)
{Electric field inside an isolated capacitor decreases after inserting a dielectric.} For an isolated capacitor, charge remains constant. Insertion of dielectric increases capacitance, so: \[ E = \frac{\sigma}{\varepsilon_0 \varepsilon_r} \] Electric field decreases by factor \(\varepsilon_r\). \(\Rightarrow\) True
(D)
{Displacement of charge does not happen when a dielectric is inserted in an isolated capacitor because dielectric acts like an insulator.} No free charge flows through the dielectric; only bound charges rearrange. Charge on plates remains unchanged. \(\Rightarrow\) True
(E)
{Energy of isolated capacitor increases when a dielectric is inserted.} For isolated capacitor: \[ U = \frac{Q^2}{2C} \] Since \(C\) increases, energy decreases. \(\Rightarrow\) False

Final Conclusion:
Correct statements are \(\boxed{A,\,B,\,C,\,D}\).