Page 1 Notes

  • Capacitance Equation:
      - Definition: The capacitance (C) of a circuit is defined as the charge (Q) per unit potential difference (V), mathematically expressed as:
        C=QVC = \frac{Q}{V}
      - Units:
        - SI unit: Farad (F)
        - C = [AT][AT] (where A = Ampere, T = Second) equal to [M−1L−2T4A2][M^{-1}L^{-2}T^{4}A^{2}]

  • Dimensionless Variables:
      - Description: Variables that have no dimensions.
        - Fundamental Dimensions:
          - Mass (M), Length (L), Time (T), Charge (A), Temperature ( ), Amount of substance (mol), Luminous intensity (cd)
      - Example: c/18c/18 (unit-specific mention, clarify context)

  • Refractive Index:
      - Definition: The refractive index (n) is a dimensionless number that describes how fast light travels in a medium compared to vacuum.
        - Formula: n=cvn = \frac{c}{v} (c = speed of light in vacuum, v = speed in the medium)

  • Efficiency of Work:
      - Definition: Efficiency can be expressed as the ratio of output work to input work.
        - Mathematical representation:
          Efficiency=Output WorkInput Work\text{Efficiency} = \frac{\text{Output Work}}{\text{Input Work}}
      - Strain:
        - Definition: Change in length per original length strain=ΔLL0\text{strain} = \frac{\Delta L}{L_{0}}
      - Units: Strain is dimensionless since it is a ratio of lengths.

Page 2 Notes

  • Energy Equations:
      - Energy derived from work:
        - Work (W):
          W=F⋅dW = F \cdot d
      - Work units: [M2T−2][M^2 T^{-2}]

  • Power:
      - Definition: Power is the rate of doing work or transferring energy.
        - Equation:
          P=WtP = \frac{W}{t}
      - Units:
        - SI unit: Watt (W) [M1L2T−3][M^1 L^2 T^{-3}]

  • Surface Tension:
      - Defined as the force per unit length acting along the surface of a liquid.
      - Units: Surface tension=FL\text{Surface tension} = \frac{F}{L} [N/m][N/m]

  • Viscous Force Equation:
      - F=μAVLF = \mu A \frac{V}{L}
        - Where:
          - F = viscous force
          - A = area
          - μ\mu = coefficient of viscosity
          - V = velocity
          - L = characteristic length

  • Pressure:
      - Formula: P=FAP = \frac{F}{A}
      - Units: [ML−1T−2][ML^{-1}T^{-2}]

Page 3 Notes

  • Dimensional Analysis:
      - Definition: It is the analysis of the relationship of a physical quantity with the fundamental dimensions. Dimensions are represented using square brackets.
      - Example: Velocity is defined as:
        Velocity=displacementtime\text{Velocity} = \frac{\text{displacement}}{\text{time}} [LT−1][LT^{-1}]
      - Acceleration:
        - Defined as the rate of change of velocity, expressed as:
          Acceleration=VelocityTime\text{Acceleration} = \frac{\text{Velocity}}{\text{Time}}
          [LT−2][LT^{-2}]

  • Force:
      - Definition: Force is defined by Newton's second law:
        F=m⋅aF = m \cdot a
        - Units: F=[MLT−2]F = [MLT^{-2}]
      - Work:
        - Work is defined as force applied over a distance:
          W=F⋅dW = F \cdot d
        - Units: [ML2T−2][ML^2T^{-2}]
      - Torque:
        - Defined as the product of force and distance from the pivot point:
          Torque=F⋅r\text{Torque} = F \cdot r
          [ML2T−2][ML^2T^{-2}]

Page 4 Notes

  • Units of Time:
      - Millenium: 1000 years (largest unit of time)
      - Shake: 10−810^{-8} seconds (smallest unit of time)

  • SI Prefixes:
      - Describes powers of ten used in measurement:
      - Example:
        - Exa: 101810^{18} (Symbol: E)
        - Peta: 101510^{15} (P)
        - Tera: 101210^{12} (T)
        - Giga: 10910^{9} (G)
        - Mega: 10610^{6} (M)
        - Kilo: 10310^{3} (k)
        - Hecto: 10210^{2} (h)
        - Deca: 10110^{1} (da)
        - Deci: 10−110^{-1} (d)
        - Centi: 10−210^{-2} (c)
        - Milli: 10−310^{-3} (m)
        - Micro: 10−610^{-6} (μ)
        - Nano: 10−910^{-9} (n)
        - Pico: 10−1210^{-12} (p)
        - Femto: 10−1510^{-15} (f)
        - Atto: 10−1810^{-18} (a)

  • Example of Scientific Notation:
      - The number 3492 km can be represented as:
        3.492×1033.492 \times 10^{3} km

Page 5 Notes

  • Unit of Mass:
      - 100g = 1 New system unit (to clarify new context)

  • Volume Calculations:
      - Example of converting to new units:
        - If new unit for volume is 100cm3100 cm^{3}, conversions seen in expressions.

  • Measurement Variables and Constants:
      - Use of equations to derive relationships across different measurement systems.

Page 6 Notes

  • Equations Validity:
      - General rule: An equation is valid only if every operation has the same units.
        - Example: For the equation vf=vi+atv_f = v_i + at, all terms must share the same units of measurement.

  • Special Units of Length:
      - Astronomical unit (AU) = 1.496imes10111.496 imes 10^{11} m
      - Light year = 9.46imes10159.46 imes 10^{15} m
      - Parsec = approx. 3.086 x 10^{16} m
      - Permi = 10−1510^{-15} m (smallest practical unit of length)

Page 7 Notes

  • Derived Units:
      - Area: A=L×L=m2A = L \times L = m^{2}
      - Volume: V=L×L×L=m3V = L \times L \times L = m^{3}
      - Velocity: Displacement/time = m/sm/s
      - Acceleration: Change in velocity over time = m/s2m/s^{2}
      - Force: Defined as mass multiplied by acceleration = F=m⋅a=kgimesm/s2F = m \cdot a = kg imes m/s^{2}

  • Unit Conversion:
      - Conversion for same measurement was shown as n1=n2v2n_{1} = n_{2}v_{2} (Law of conservation across systems)

Page 8 Notes

  • Measurement Definition:
      - The process of comparing an unknown quantity with a known standard.
      - The standard used is called a unit.

  • Measurement Systems:
      - CGS (Centimeter, Gram, Second)
      - FPS (Foot, Pound, Second)
      - SI (Metre, Kilogram, Second)

Page 9 Notes

  • Physical Quantities Classification:
      - Fundamental Quantities: Basic independent quantities such as mass, length, etc.
        - Units categorized as Fundamental Units
      - Derived Quantities: Quantities derived from fundamental quantities expressed in terms of fundamental units such as speed, energy, etc.
      - Supplementary Quantities: Plane angle, solid angle, etc.

  • Fundamental Quantities Overview:
      - Independent and cohesive units necessary for measurement standards.

Capacitance, Energy, and Units:

  • Capacitance: Think of it like a container for electricity. It tells us how much electric charge we can store in it for a certain amount of push (or voltage). It's like how much water a bucket can hold when we fill it up with a hose.

  • What is Energy?: Energy is like the fuel that allows things to happen. If you push a toy car, you use energy to make it move. The energy could come from your muscles or from batteries.

  • Power: Imagine you’re riding your bike. Power tells us how fast you’re going while pedaling. If you pedal a lot and really fast, you use more power! It shows how much work you do over time.

  • Force: When you push something, like a friend on a swing, you’re using force. It’s how hard you’re pushing or pulling.

  • Pressure: This is what happens when you push down on something. If you put your hand on a balloon, you’re making pressure on it.

Different Measurements:

  • Units: We use units to measure things. For example, we can measure how heavy something is in kilograms or how long it is in meters. It’s like using cups for measuring ingredients when cooking.

  • Time: We measure time in seconds, minutes, and hours. Think of it like watching the clock for when snack time happens!

  • Volume: This tells us how much space something takes up. Like how much water fits in a glass. We can measure this in milliliters or liters.

  • Weight: This is how heavy something is. Like a bag of sugar can weigh 1 kg. It tells us how much gravity is pulling on it.

Science can be complicated, but it helps us understand the world around us! When we measure everything, it makes it easier to explain and understand how things work. Just like how we might say, "Let's make a big cake and we've got to measure our ingredients just right."