An electrical circuit is shown in fig the values of...

An electrical circuit is shown in fig the values of resistances and the directions of the currents are shown $\mathrm{A}$ voltmeter of resistance $400 \Omega$ is connected across the $400 \Omega$ resistor. The battery has negligible internal resistance.The value of current $\mathrm{i}_{2}$ is (A) $(1 / 30) \mathrm{A}$ (B) $(1 / 15) \mathrm{A}$ (C) $(1 / 10) \mathrm{A}$ (D) $(2 / 15) \mathrm{A}$

An electrical circuit is shown in fig the values of resistances and the directions of the currents are shown $\mathrm{A}$ voltmeter of resistance $400 \Omega$ is connected across the $400 \Omega$ resistor. The battery has negligible internal resistance.The value of current $\mathrm{i}_{2}$ is
(A) $(1 / 30) \mathrm{A}$
(B) $(1 / 15) \mathrm{A}$
(C) $(1 / 10) \mathrm{A}$
(D) $(2 / 15) \mathrm{A}$

Key Concepts

Current Division

The current division principle describes how the total current entering a parallel network splits among the parallel branches. The amount of current through each branch is inversely proportional to its resistance. This concept enables the calculation of branch currents in multi-path circuits, which is vital for solving problems involving parallel resistors.

Instrument Loading Effects

When measuring circuit parameters, instruments such as voltmeters and ammeters can affect the circuit's behavior. The loading effect occurs when a voltmeter with finite resistance is connected across a circuit element, effectively altering the resistance seen by the circuit. Understanding this impact is essential to ensure that measurements reflect the true behavior of the circuit.

Kirchhoff's Circuit Laws

Kirchhoff's Circuit Laws, which consist of the Current Law (KCL) and Voltage Law (KVL), are essential tools for analyzing complex circuits. KCL states that the total current entering a junction must equal the total current leaving the junction, while KVL asserts that the sum of the electrical potential differences (voltage) around any closed network is zero. These laws help set up the equations needed to solve for unknown currents and voltages in a circuit.

Ohm's Law

Ohm's Law is a fundamental principle in electrical engineering that relates voltage, current, and resistance in a circuit. It is typically expressed as V = IR, where V is voltage, I is current, and R is resistance. This law underpins much of circuit analysis by allowing the calculation of any one of these quantities if the other two are known, which is crucial for solving problems in resistive circuits.

Series and Parallel Resistor Combinations

Resistors in a circuit can be connected in series or in parallel. In series, resistances add directly, resulting in a higher total resistance, while in parallel, the inverse of the total resistance is the sum of the inverses of the individual resistances. Understanding these combinations is critical for determining the overall resistance of a circuit and for accurately analyzing current paths.

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