4.3 Kirchhoff's Laws & Magnetism

Why Kirchhoff's Laws Matter

Series and parallel rules from section 4.2 solve many circuits, but real electrical systems — including shipboard distribution panels with multiple loads and feed points — often have more than one loop or more than two paths meeting at a junction. Kirchhoff's Laws, named for German physicist Gustav Kirchhoff, give you the tools to analyze any circuit, no matter how complex, and they are explicitly flagged as a core NAPT electricity topic.

Kirchhoff's Current Law (KCL)

Kirchhoff's Current Law (KCL) states that the sum of currents entering a junction (node) equals the sum of currents leaving it. This is simply a statement of conservation of electric charge: charge cannot pile up or disappear at a junction, so whatever flows in must flow out.

Worked Example: A distribution junction has 15 A flowing in from the main feeder. It splits into two branch circuits. Branch 1 carries 9 A. How much current flows through Branch 2?

By KCL: I_in = I_out, so 15 A = 9 A + I2, which gives I2 = 6 A

Kirchhoff's Voltage Law (KVL)

Kirchhoff's Voltage Law (KVL) states that the sum of all voltage rises and drops around any closed loop in a circuit equals zero. This is a statement of conservation of energy: whatever electrical push a voltage source supplies to a loop must be completely used up by the resistive drops around that same loop.

Worked Example: A single-loop circuit has a 24V battery connected in series with three resistors: R1 = 2Ω, R2 = 3Ω, and R3 = 7Ω. Find the current and confirm KVL holds.

R_total = R1 + R2 + R3 = 2 + 3 + 7 = 12 Ω I = V/R_total = 24 V ÷ 12 Ω = 2 A V1 = I × R1 = 2 × 2 = 4 V V2 = I × R2 = 2 × 3 = 6 V V3 = I × R3 = 2 × 7 = 14 V

KVL equation: EMF − V1 − V2 − V3 = 0 → 24 − 4 − 6 − 14 = 0 (confirmed)

The voltage drops (4 V + 6 V + 14 V = 24 V) exactly account for all the energy the battery supplies — nothing is created or lost, it is only converted into heat across each resistor. Notice this is the same check used in section 4.2's series circuit example; KVL is simply the formal law behind that pattern.

Basic Magnetism and Electromagnetism

A magnetic field is a region of space around a magnet or a current-carrying conductor where a magnetic force can be detected. Magnetic field lines run from a magnet's north pole to its south pole outside the magnet. Two fundamental rules govern how magnets interact:

• Like poles repel (north-north or south-south push apart)
• Unlike poles attract (north-south pull together)

In 1820, Danish physicist Hans Christian Oersted discovered that an electric current flowing through a conductor generates a magnetic field around that conductor — the foundational link between electricity and magnetism, and the basis for the entire field of electromagnetism. The right-hand rule gives the field's direction for a straight current-carrying wire: point your right thumb in the direction of conventional current flow, and your curled fingers show the direction the magnetic field circles the wire.

Coiling a current-carrying wire into a loop, or many loops (a solenoid), concentrates and strengthens the magnetic field produced. Adding a ferromagnetic core, such as iron, inside the coil strengthens the field further. This is the basic operating principle behind electromagnets, electric motors, generators, and relays — and, at a larger scale, the degaussing coils used aboard Navy ships to reduce a vessel's own magnetic signature.

Understanding this electricity-magnetism link matters beyond the test: every electric motor and generator aboard a ship converts between electrical and mechanical energy by exploiting exactly this relationship.