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 $\mathrm{R}_{1}=6, \mathrm{R}_{4}=3 \mathrm{Ohm}$ $\mathrm{R}_{3}=4, \mathrm{R}_{2}=2$ 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$ $\mathrm{R}_{2}=2 \Omega \quad \mathrm{R}_{3}=4 \Omega \quad \mathrm{R}_{4}=3 \Omega$ The current through resistance $\mathrm{R}_{3}$ is. (A) $1.5 \mathrm{~A}$ (B) $1.2 \mathrm{~A}$ (C) $0.9 \mathrm{~A}$ (D) $0.6 \mathrm{~A}$

The circuit shown in fig consists of the following $E_{1}=6, E_{2}=2, E_{3}=3$ Volt
$\mathrm{R}_{1}=6, \mathrm{R}_{4}=3 \mathrm{Ohm}$
$\mathrm{R}_{3}=4, \mathrm{R}_{2}=2$ 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$
$\mathrm{R}_{2}=2 \Omega \quad \mathrm{R}_{3}=4 \Omega \quad \mathrm{R}_{4}=3 \Omega$
The current through resistance $\mathrm{R}_{3}$ is.
(A) $1.5 \mathrm{~A}$
(B) $1.2 \mathrm{~A}$
(C) $0.9 \mathrm{~A}$
(D) $0.6 \mathrm{~A}$

Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits stating that the voltage across a resistor is directly proportional to the current through it and its resistance, expressed as V = IR. This law is crucial for calculating currents, voltages, or resistances in various portions of a circuit.

Kirchhoff's Laws

Kirchhoff's Laws are essential tools in circuit analysis. Kirchhoff's Voltage Law (KVL) asserts that the sum of all voltage drops in a closed loop must equal the total electromotive force in that loop, while Kirchhoff's Current Law (KCL) states that the total current entering a junction must equal the current leaving. These principles enable the formulation of equations to solve for unknown currents and voltages in complex circuits.

Series and Parallel Resistor Combinations

Understanding how resistors combine in series and parallel is fundamental to simplifying circuits. In series, resistances add directly, while in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances. This method of circuit simplification is key to analyzing the overall behavior of a network of resistors.

DC Steady-State Behavior of Capacitors

In DC circuits, capacitors reach a steady state where they become fully charged and effectively act as open circuits, thereby blocking direct current. Recognizing this behavior is important when analyzing circuits that include capacitors, as it allows for the simplification of the circuit by removing the capacitor’s influence on the DC current paths.

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