Two air capacitors A=1 μF, B=4 μF are connected in series with 35 V source. When a medium of di

step 1 Initially, A and B are in series. So I can write 1 by CS is equal to 1 by 1 plus 1 by 4, which i

Two air capacitors A=1 μF, B=4 μF are connected in series...

Two air capacitors $A=1 \mu F, B=4 \mu F$ are connected in series with $35 \mathrm{~V}$ source. When a medium of dielectric constant $\mathrm{K}=3$ is introduced between the plates of $\mathrm{A}$, change on the capacitor changes by (A) $16 \mu \mathrm{c}$ (B) $32 \mu \mathrm{c}$ (C) $28 \mu \mathrm{c}$ (D) $60 \mu \mathrm{c}$

Two air capacitors $A=1 \mu F, B=4 \mu F$ are connected in series with $35 \mathrm{~V}$ source. When a medium of dielectric constant $\mathrm{K}=3$ is introduced between the plates of $\mathrm{A}$, change on the capacitor changes by
(A) $16 \mu \mathrm{c}$
(B) $32 \mu \mathrm{c}$
(C) $28 \mu \mathrm{c}$
(D) $60 \mu \mathrm{c}$

Key Concepts

Series Connection of Capacitors

In a series circuit, capacitors are connected one after the other so that the same charge flows through each capacitor, but the voltage across each capacitor can vary. The overall or equivalent capacitance of the series combination is determined by the reciprocal sum of the individual capacitances, leading to a value that is always less than the smallest individual capacitor in the series. This concept is foundational when analyzing how voltage divides and charge distributes across series-connected components.

Equivalent Capacitance

The equivalent capacitance of a network of capacitors simplifies a complex circuit into a single capacitor that stores the same total charge under the same applied voltage. For series-connected capacitors, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances. This concept allows engineers to analyze circuits by reducing multiple capacitors to one, particularly when evaluating the effects of changes within one part of the circuit.

Dielectric Constant

A dielectric constant is a property of an insulating material, indicating how much the material can increase a capacitor's ability to store charge compared to air or vacuum. When a dielectric is introduced between the plates of a capacitor, the capacitance increases by a factor equal to the dielectric constant, reflecting the material's capacity to reduce the electric field and hence increase charge storage for the same applied voltage.

Charge Redistribution in Series Capacitors with a Dielectric

In a series circuit, the introduction of a dielectric in one capacitor alters its capacitance, which in turn affects the overall equivalent capacitance of the series. Since the same charge flows through all capacitors in a series, the alteration in capacitance leads to a redistribution of voltage across the individual capacitors. The change in charge on an individual capacitor, when a dielectric is inserted, is analyzed by comparing the circuit before and after the introduction, reflecting the impact of the increased capacitance due to the dielectric material.

Please give Ace some feedback