Vector Analysis

4 vector operations Addition of two vectors Commutative: $\textbf{A + B = B + A}$ Associative: $\textbf{(A + B) + C = A + (B + C)}$ Multiplication by a scalar Distributive: $a(\textbf{A + B}) = a\textbf{A} + a\textbf{B}$, where a is a scalar Dot product of two vectors (Also known as scalar product) $\textbf{A . B} = \left|A\right|\left|B\right|cos \theta$ Commutative: …

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SS: Electric Circuits and symbols

An electric circuit is a collection of electrical devices, called circuit elements connected by conductors in a closed path (i.e., in a complete loop). Circuit elements include, source of electrical energy (e.g. battery), sink of electrical energy (e.g. light bulb), and switch to complete or break the circuit. Conductors (e.g., copper wires) are then used to connect them together. Electrical …

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SS: Direct and alternating current

A direct current (DC) is a flow of charges around a circuit in the same direction all the time. Batteries supply DC and most appliances need DC to function.   Alternating current (AC) is a flow of charges around a circuit that reverses its direction at regular intervals, usually many times a second. Household electrical power is supplied in the …

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D.C. Circuits (O Level)

This topic covers “DC Circuits” of O Level Physics. (Equivalent to American high school diploma) If this is too basic for you, you can try the more advanced version here. Sub-Topics: Direct and alternating current Electric Circuits and symbols Series and parallel circuits Quiz: Quiz For Static Electricity, Current Electricity, D.C. Circuits and Practical Electric Circuitry

SS: Boyle’s Law

Boyle’s Law states that the volume of a fixed mass of gas at constant temperature is inversely proportional to the pressure applied to the gas. $$pV = \text{constant}$$ $$p_{1}V_{1} = p_{2}V_{2}$$ where $p_{1}$ = initial pressure $V_{1}$ = initial volume $p_{2}$ = final pressure $V_{2}$ = final volume A more detailed treatment of Boyle’s Law can be found in Pressure …

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SS: Hydraulic systems

Car lift One simple application is shown in the diagram above, the lifting of a car. If there is a relatively small force $F_{1}$, pushing down on piston $A_{1}$, the pressure on the fluid is $p_{1} = \frac{F_{1}}{A_{1}}$. The pressure is transmitted via the incompressible fluid to the other piston $A_{2}$: $$\begin{aligned} p_{1} &= p_{2} \\ \frac{F_{1}}{A_{1}} &= \frac{F_{2}}{A_{2}} \\ …

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