A battery of emf 10 V is connected to resistances as shown...

A battery of emf $10 \mathrm{~V}$ is connected to resistances as shown in the following figure. The potential difference between $A$ and $B,\left(V_{A}-V_{B}\right)$ is
(a) $-2 \mathrm{~V}$
(b) $2 \mathrm{~V}$
(c) $5 \mathrm{~V}$
(d) $(20 / 11) \mathrm{V}$

Key Concepts

Voltage Divider Rule

The voltage divider rule is a specific application of Ohm's Law in series circuits that allows the calculation of the voltage drop across a particular resistor. By knowing the total voltage across a series network and the resistance of each component, the voltage divider rule helps identify how the input voltage is proportionally distributed among the series elements.

Series and Parallel Circuits

Understanding how resistors are connected in series and parallel is vital for accurate circuit analysis. In series circuits, resistances add directly, and the same current flows through each resistor, influencing the overall voltage drop. In parallel circuits, the voltage across each resistor remains the same, and the total current is divided among the branches, affecting how the circuit’s equivalent resistance is computed.

Ohm's Law

Ohm's Law states that the voltage across a resistor is directly proportional to the current flowing through it, expressed as V = I × R. This concept is fundamental in circuit analysis as it provides the basic relationship needed to compute voltage drops across resistive elements in any electrical circuit.

Kirchhoff's Voltage Law (KVL)

Kirchhoff's Voltage Law asserts that the sum of all potential differences around any closed loop in a circuit is zero. This principle is crucial for analyzing circuits as it allows the determination of unknown voltages by setting up equations based on the known voltage sources and the voltage drops across resistors in the loop.

Kirchhoff's Current Law (KCL)

Kirchhoff's Current Law states that the total current entering a junction or node in an electrical circuit must equal the total current leaving that junction. This law is essential for analyzing how currents split or combine at various nodes, ensuring the conservation of electric charge throughout the circuit.

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