Ethan sat attentively as the Librarian prepared to explain the derived SI units, which build upon the fundamental ones to describe more complex quantities.
The Librarian opened the book, and a detailed table appeared in the air, illustrating various derived SI units and their relationships to the fundamental units.
"Today," the Librarian began, "we will explore the derived SI units—quantities that are derived from the seven base units. These units are used to measure a wide range of physical properties."
The Librarian pointed to the first entry in the chart. "Magnetic Flux (Φ) is measured in Webers (Wb). One Weber is equal to one volt-second or one kilogram meter squared per second squared per ampere. This unit describes the total magnetic field passing through a surface."
The chart shifted to the next unit. "Magnetic Flux Density (B) is measured in Teslas (T). One Tesla is one Weber per square meter, or one kilogram per second squared per ampere. It describes the strength of the magnetic field."
"Inductance (L)," continued the Librarian, "is measured in Henrys (H). One Henry is one Weber per ampere or one volt-second per ampere. This unit measures how much a coil resists changes in current."
The Librarian moved on. "Luminous Flux (Φv) is measured in Lumens (lm). One Lumen is one candela steradian. It represents the total amount of visible light emitted."
"Illuminance (E)," said the Librarian, "is measured in Lux (lx). One Lux is one Lumen per square meter, indicating how much light falls on a given area."
Next, the Librarian explained, "Activity (of a radioactive substance) (A) is measured in Becquerels (Bq). One Becquerel is one decay per second, quantifying the rate of radioactive decay."
"Absorbed Dose (D)," the Librarian continued, "is measured in Grays (Gy). One Gray is one joule per kilogram, indicating how much radiation energy is absorbed per unit mass."
"Electric Capacitance (C)," the Librarian said, "is measured in Farads (F). One Farad is one ampere-second per volt, describing a capacitor's ability to store charge."
The chart then showed additional derived units. "Plane Angle (θ) is measured in Radians (rad), which is dimensionless, representing the ratio of the arc length to the radius."
"Solid Angle (Ω) is measured in Steradians (sr), also dimensionless, representing the area of the sphere's surface subtended by an angle."
"Frequency (f) is measured in Hertz (Hz), which is one cycle per second."
"Force (F) is measured in Newtons (N). One Newton is one kilogram meter per second squared, measuring the push or pull on an object."
"Pressure (p) is measured in Pascals (Pa). One Pascal is one Newton per square meter, representing the force per unit area."
"Energy, Work, and Heat (E, W, Q) are measured in Joules (J). One Joule is one Newton meter, representing the amount of work done."
"Power and Radiant Flux (P) are measured in Watts (W). One Watt is one Joule per second, indicating the rate of energy transfer."
"Electric Charge (Q) is measured in Coulombs (C). One Coulomb is one ampere-second, quantifying the amount of electric charge."
"Electric Potential and Electromotive Force (U, V) are measured in Volts (V). One Volt is one Watt per ampere, representing the electric potential difference."
"Electrical Resistance (R) is measured in Ohms (Ω). One Ohm is one Volt per ampere, indicating how much a conductor resists electric current."
Finally, the Librarian said, "Electrical Conductance (G) is measured in Siemens (S). One Siemens is the reciprocal of an Ohm, or one second cubed ampere squared per kilogram meter squared."
The chart faded, leaving Ethan with a comprehensive understanding of how these derived units build upon the fundamental ones to measure various physical phenomena.
"These derived units," the Librarian explained, "are essential for expressing complex quantities in engineering and science. They allow us to describe and analyze the world in precise and meaningful ways."
Ethan absorbed the information, appreciating how these units fit into the broader framework of measurement.