The circuit shown in fig consists of the following E1=6,...

The circuit shown in fig consists of the following $E_{1}=6, E_{2}=2, E_{3}=3$ Volt $\mathrm{R}_{1}=6, \mathrm{R}_{4}=3 \mathrm{Ohm}$ $\mathrm{R}_{3}=4, \mathrm{R}_{2}=2 \mathrm{Ohm}$ $\mathrm{C}=5 \mu \mathrm{F}$$E_{1}=6 \mathrm{~V} \quad E_{2}=2 \mathrm{~V} \quad E_{3}=3 \mathrm{~V} \quad \mathrm{R}_{1}=6 \Omega$ $R_{2}=2 \Omega \quad R_{3}=4 \Omega \quad R_{4}=3 \Omega$ The energy stored in the capacitor is. (A) $4.8 \times 10^{-6} \mathrm{~J}$ (B) $9.6 \times 10^{-6} \mathrm{~J}$ (C) $1.44 \times 10^{-5} \mathrm{~J}$ (D) $1.92 \times 10^{-5} \mathrm{~J}$

The circuit shown in fig consists of the following $E_{1}=6, E_{2}=2, E_{3}=3$ Volt
$\mathrm{R}_{1}=6, \mathrm{R}_{4}=3 \mathrm{Ohm}$
$\mathrm{R}_{3}=4, \mathrm{R}_{2}=2 \mathrm{Ohm}$
$\mathrm{C}=5 \mu \mathrm{F}$$E_{1}=6 \mathrm{~V} \quad E_{2}=2 \mathrm{~V} \quad E_{3}=3 \mathrm{~V} \quad \mathrm{R}_{1}=6 \Omega$
$R_{2}=2 \Omega \quad R_{3}=4 \Omega \quad R_{4}=3 \Omega$
The energy stored in the capacitor is.
(A) $4.8 \times 10^{-6} \mathrm{~J}$
(B) $9.6 \times 10^{-6} \mathrm{~J}$
(C) $1.44 \times 10^{-5} \mathrm{~J}$
(D) $1.92 \times 10^{-5} \mathrm{~J}$

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Key Concepts

Capacitor Energy Storage

This concept refers to the method of calculating the energy stored in a capacitor using the formula E = 1/2 CV², where C is the capacitance and V is the voltage across the capacitor. Understanding this formula is essential for determining how much energy is stored based on the voltage across the device, which is a fundamental concept in circuits involving energy storage components.

DC Steady-State Analysis

In DC circuits that include capacitors, once the transient effects have died out, capacitors behave as open circuits. This means that in a steady-state condition, no current flows through the capacitor, and the voltage across it remains constant. This principle is important for correctly analyzing circuits to determine the voltage that appears across the capacitor at equilibrium.

Circuit Analysis Techniques

Techniques such as Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) are used to analyze complex circuits and determine the distribution of voltages and currents. These methods, which may include node voltage analysis or mesh current analysis, are crucial for calculating the exact voltage that charges the capacitor in the circuit, thereby allowing for the correct application of the capacitor energy storage formula.

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