Ampere's circuital law and applications (solenoid, toroid, wire) is a core Magnetism & Magnetic Effects of Current concept in Physics. This guide explains what it is, walks through a fully worked example, and lists the key equations you need — with a short quiz to test yourself.

Key equations and worked example

A 6 V battery across a 10 Ω resistor drives I = V/R = 0.6 A. Double the voltage to 12 V and the current doubles to 1.2 A — Ohm's law is linear. The power dissipated as heat is P = V·I = 7.2 W, which is why the resistor in the simulator warms the idea up: raise the voltage slider and watch the electrons speed up.

• <code>Ohm&#39;s law: V = I·R</code>
• <code>Current: I = Q / t</code>
• <code>Power: P = V·I = I²·R = V²/R</code>
• <code>Series: R_total = R₁ + R₂; Parallel: 1/R_total = 1/R₁ + 1/R₂</code>

Ampere&#39;s circuital law and applications (solenoid, toroid, wire) in detail

Ampere&#39;s circuital law and applications (solenoid, toroid, wire) is one of the central ideas in Magnetism &amp; Magnetic Effects of Current, and it appears in Physics curricula under Magnetic field and forces. It is worth learning deeply because it connects to so many other topics in this section.

Current is the rate of charge flow (I = Q/t, measured in amperes). In a metal, a voltage across the conductor pushes free electrons into a slow drift — their collisions with ions are what we call resistance. Ohm&#39;s law (V = IR) holds for ohmic conductors at constant temperature: double the voltage, double the current. The battery&#39;s chemical energy becomes the electrons&#39; kinetic energy, then heat and light in the components.

For exams, the pattern is predictable: first a definition or statement of the result, then a direct numerical application of one of the equations above, then a "why" question — why the formula takes that form, or what changes when a variable is doubled or halved. The worked example and quiz below cover exactly that progression.

Quick self-check:

• Q: State Ohm&#39;s law and the condition for it to hold.<br />A: V = IR; it holds for ohmic conductors at constant temperature (linear V–I graph through the origin).
• Q: A 12 V battery drives 2 A through a resistor. What is the resistance and power?<br />A: R = V/I = 6 Ω; P = V·I = 24 W.
• Q: Why do electrons drift slowly even though the signal travels near light speed?<br />A: The electric field propagates fast, but each electron only drifts mm/s, constantly colliding with ions — those collisions are resistance.
• Q: How does adding resistors in series change the current?<br />A: Total resistance rises (R₁+R₂), so for the same voltage the current falls: I = V/(R₁+R₂).