Derived SI units are units of measurement in the International System of Units (SI) that are formed by combining base SI units using mathematical operations. These derived units represent physical quantities that are derived from fundamental quantities like length, mass, time, electric current, temperature, amount of substance, and luminous intensity. Some common derived SI units include:

** Area (m²)**: The derived unit for area is the square meter (m²), which is the area of a square with sides of one meter.

** Volume (m³)**: The derived unit for volume is the cubic meter (m³), which is the volume of a cube with sides of one meter. Other units like liters (L) and milliliters (mL) are also commonly used for measuring volume, although they are not SI units.

** Velocity (m/s)**: The derived unit for velocity is meters per second (m/s), which represents the distance traveled per unit of time.

**Acceleration (m/s²)**: The derived unit for acceleration is meters per second squared (m/s²), which represents the change in velocity per unit of time.

**Force (N)**: The derived unit for force is the newton (N), which is defined as the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second squared.

**Pressure (Pa)**: The derived unit for pressure is the pascal (Pa), which is defined as one newton per square meter.

**Energy (J)**: The derived unit for energy is the joule (J), which is defined as the work done by a force of one newton acting over a distance of one meter. J = Nm

**Power (W)**: The derived unit for power is the watt (W), which is defined as one joule per second. W = J/s

**Electric Charge (C)**: One coulomb is defined as the amount of electric charge that passes through a surface in an electric circuit in one second when a current of one ampere is flowing through the circuit. 1 Coulomb=1 Ampere × 1 Second

**Electric Potential (V)**: The volt is the derived unit for electromotive force and is defined as the multiplicand of an electrical current measured in Ampere, through a resistance of 1 Ohm

**Electric Capacitance (F)**: One farad (1 F) is defined as the capacitance of a capacitor that stores one coulomb (1 C) of electrical charge when a potential difference of one volt (1 V) is applied across its terminals. Mathematically, it can be expressed as:

**Electric Resistance (R or** ) Where: R is the resistance in ohms (Ω), V is the voltage across the component in volts (V) and I is the current flowing through the component in amperes (A).

**Frequency (Hz)**: Frequency f is expressed as:

Where: f is the frequency in hertz (Hz) (Cycles per Second)and T is the period of the waveform in seconds (s), which is the time taken for one complete cycle of the waveform.

**Magnetic Flux (Wb)**: Magnetic Flux Through a Closed Surface (Flux Density):

When a magnetic field passes through a closed surface, the magnetic flux is given by the product of the magnetic flux density BB and the surface area AA perpendicular to the magnetic field. Mathematically, it can be expressed as: Φ=B⋅A

Where:

Φ is the magnetic flux in webers (Wb).

B is the magnetic flux density in teslas (T).

A is the area perpendicular to the magnetic field in square meters (m²).

Magnetic Flux Through an Open Surface (Flux Linkage):

When a varying magnetic field passes through a coil or a conductor, the magnetic flux through the coil is called the magnetic flux linkage. It is given by the product of the magnetic flux density BB, the number of turns in the coil NN, and the area AA perpendicular to the magnetic field. Mathematically, it can be expressed as: Φ=B⋅A⋅N

Where:

Φ is the magnetic flux in webers (Wb).

B is the magnetic flux density in teslas (T).

A is the area perpendicular to the magnetic field in square meters (m²).

N is the number of turns in the coil.

**Magnetic Flux Density (T (Tesla))** One tesla is defined as the magnetic flux density that results in a force of one newton (N) acting on a one-meter-long conductor carrying a current of one ampere (A) perpendicular to the magnetic field. It is expressed as:

**Inductance (H (Henry))** is defined as the inductance of a closed circuit in which an electromotive force of one volt is produced when the electric current in the circuit varies uniformly at a rate of one ampere per second. Mathematically, it is expressed as:

These derived units, along with the base SI units, form the foundation of the SI system and are used to express a wide range of physical quantities in various fields of science, engineering, and everyday life.

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