A detailed Informative Account on SI Units

**SI Base Units**

All quantities in science consist of a number and a unit. There is a system of units

used throughout the scientific world known as SI units. SI units are based on the

units of six base quantities:

All quantities in Science consist of a magnitude and a Unit. The system for units used across the world is known as SI Units. SI units are based on seven base quantities.

- Length – meter (m)
- Time – second (s)
- Amount of substance – mole (mole)
- Electric current – ampere (A)
- Temperature – kelvin (K)
- Luminous intensity – candela (cd)
- Mass – kilogram (kg)

Degree Celcius is a unit most commonly known and used but it’s not an SI unit.

In general physics, many units are used for measuring different quantities like Pressure, Velocity, Weight, acceleration, and joules these are **Derived Units.**

### Derived Units

Derived units are results of mathematical calculations of SI units under the Laws and theorems of Physics. For example Velocity = Displacement/Time

V = displacement in meter/ time in seconds resulting in m/s. Acceleration is derived by the Formula Acceleration = Velocity/ time resulting in its unit m/s^{2}

Here is a list of some physical quantities you should know:

Physical Quantity | Name | Symbol | Expressed in SI Base Units |
---|---|---|---|

frequency | hertz | Hz | s^{-1} |

force | newton | N | m kg s^{-2} |

pressure, stress | pascal | Pa | N m^{-2} = m^{-1} kg s^{-2} |

energy, work, heat | joule | J | N m = m^{2} kg s^{-2} |

power, radiant flux | watt | W | J s-1 = m^{2} kg s^{-3} |

electrical charge | coulomb | C | A s |

electrical potential, electromotive force | volt | V | J C-1 = m^{2} kg s^{-3} A^{-1} |

electrical resistance | ohm | Ω | V A^{-1} = m^{2} kg s^{-3} A^{-2} |

electric conductance | siemens | S | ohm^{-1} = m^{-2} kg^{-1} s^{3} A^{2} |

electrical capacitance | farad | F | C V^{-1} = m^{-2} kg^{-1} s^{4} A^{2} |

magnetic flux density | tesla | T | V s m^{-2} = kg s^{-2} A^{-1} |

magnetic flux | weber | Wb | V s = m^{2} kg s^{-2} A^{-1} |

inductance | henry | H | V A^{-1} s = m^{2} kg s^{-2} A^{-2} |

luminous flux | lumen | lm | cd sr |

illuminance | lux | lx | cd sr m^{-2} |

radioactive activity | becquerel | bq | s^{-1} |

absorbed dose of radiation | gray | Gy | J kg^{-1} = m^{2} s^{-2} |

dose equivalent of radiation | sievert | Sv | J kg^{-1} = m^{2} s^{-2} |

plane angle | radian | rad | 1 m m^{-1} |

solid angle | steradian | sr | 1 m^{2} m^{-2} |

area | square metre | A | m^{2} |

volume | cubic metre | V | m^{3} |

speed, velocity | metre per second | v | m/s |

acceleration | metre per second squared | a | m/s^{2} |

wavenumber | reciprocal metre | σ | m^{–1} |

density, mass density | kilogram per cubic metre | ρ | kg/m^{3} |

surface density | kilogram per square metre | ρ_{A} | kg/m^{2} |

specific volume | cubic metre per kilogram | v | m^{3}/kg |

current density | ampere per square metre | j | A/m^{2} |

magnetic field strength | ampere per metre | H | A/m |

concentration | mole per cubic metre | c | mol/m^{3} |

mass concentration | kilogram per cubic metre | ρ, γ | kg/m^{3} |

luminance | candela per square metre | L_{v} | cd/m^{2} |

refractive index | one | n | 1 |

relative permeability | one | µ_{r} | 1 |

**Note: **Always remember Units are important for your exam. In an examination any answer without an applicable unit is unacceptable and you should always recheck your paper for units.

**Checking homogeneity of equations**If you are not sure if an equation is correct, you can use the units of the different

quantities to check it. The units on both sides of the equation must be the same.

**Using Standard Forms**

Always use Standard Forms to avoid confusion plus it’s a very efficient and easy way to cope up with large quantities and minute quantities. 15300000000000 can easily be written as 1.53 x 10^13.

**Quick Question**

Q1: Prove that the base Units for Potential Energy *Ep = mgh* and Kinetic Energy

* Ek = 1/2mv*^{2}. Show your base units.

Q2: A Thermal Power Plant is providing 5600000000 watts of energy to an area and the Voltage supplied is 250000000000mV. What is the Current supplied in Amperes?

### Multiples and submultiples of base units

Sometimes, the basic unit is either too large or too small. It would not be sensible to

use metres to measure the gap between the terminals of a spark plug in a car engine.

Instead, you would use millimetres (mm). The prefix ‘milli’ means divide by 1000 or

multiply by 10−3. Similarly, the metre would not be a sensible unit to measure the

distance between Cambridge and Hong Kong; you would use kilometres (km). Here,

the prefix is ‘kilo’, which means multiply by 1000 or 103.

These are the recognised SI prefixes. The deci- (d) prefix is often used in measuring

volume, where the decimetre cubed (dm3), is particularly useful.

Remember that 1 dm3 is 1/1000 of 1 m3 as it is 1/10 m × 1/10 m × 1/10 m.

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