Kirchoff's 2nd Law

Key Stage 5

Meaning

Kirchoff's 2nd Law states that the sum of the electromotive forces (emfs) in any closed loop is equal to the sum of potential differences (pds) in that loop.

About Kirchhoff's Second Law

• Also known as the voltage law or loop rule.
• Kirchoff's 2nd Law is based on the conservation of energy.
• Kirchoff's 2nd Law is useful for solving complex circuits with multiple loops.
• The algebraic sum of the products of the Electrical Current|currents]] and the resistances in any closed loop equals the sum of the emfs in that loop.
• Kirchoff's 2nd Law helps in setting up equations to solve for unknown voltages and currents in circuit analysis.
• Kirchoff's 2nd Law is applicable to both DC and AC circuits.
• Kirchoff's 2nd Law can be used in combination with Kirchhoff's first law for comprehensive circuit analysis.

Formula

• \(\sum V_n=V_1 + V_2 + V_3 +...=0\)

• \(\sum \varepsilon=\sum V_{pd}\)

Where:

• \(\sum V_n\) represents the sum of all voltages in a loop (including emfs and pds),

• \(V_1 + V_2 + V_3 +...\) represents the individual emfs and pds of each component in a loop,

• \(\sum \varepsilon\) represents the sum of all emfs in a loop,

• \(\sum V_{pd}\) represents the sum of all potential differences across components in a loop

Examples

• In a series circuit, the sum of the voltages across each component equals the total voltage supplied by the battery.
• Applied to find the potential differences and emfs in electrical circuits.