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Y1/Q1/Linear Circuits A/Lecture 2-Sept-24.md

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-## **Main topics:** Introduction, Basic concepts, Ohm’s law
-
-- pass the circuit labs
-	- mandatory!
-- 2 partial exams
-	- trial exam week 4
-- 6 SGH's --> only best 5 count
-	- bonus points --> dewit
-	- check [Brightspace](https://brightspace.tudelft.nl)
-
------
-# Content
-Syllabus on [Brightspace](https://brightspace.tudelft.nl)
-- Dc circuits
-	- Basis
-	- electrical elements
-	- circuit analysis methods
-- Dynamic circuits
-	- end of q1 with Time-domain solutions
-
-
------
-
-
-# Actual lecture
-#OhmsLaw 
-## The basis
-- Volta --> sustained electrical stimulus "Volta Pile"
-- move cells ("More Volts") --> more "energetic" a stimulus
-- nr of volts = voltage
-- **one always needs 2 points for tapping the energy**
-- Voltage -> 2 access points
-- An electric current deflects a magnetic needle
-- galvanometer --> precise method for measuring electric currents
-	- measures current and uses fancy math to measure volts
-- two basic, easily measurable quantities
-	- voltage + current
-- Pairs of access points
-	- at which the supplied energy
-	- between which the current
-			**Both can be unambiguousy measured** (predicted)
-	 = ports
-	Circuit analysis = the analysis of the relations between voltages and currents at given ports
-	
-We study circuits
-- made from electrical elements (lumped elements , idealized)
-- connecting wires (ideally 0 v over the wires)
-
-
-### Si system
-current -> Ampere
-Charge -> s\*A -> Coulomb (C)
-electrical potential -> volt
-
-Charge = an electrical property of sub-atomic constituents measured in Coulomb (C)
-charge of electron = e = -1.6 \* 10^-19 C
-Electric current: a measure of the temporal variation of the electric charge, measured in A(mpere)
-
-$$
-i = \frac{dq}{dt} \newline
-
-$$
-
-DC = a current that remains constant with time
-AC = current that varies sinusoidally with time
-
-A positive value for the current indicates a flow in the direction of the arrow (reference direction)
- a negative value -- \\ -- in the opposite direction of the arrow
-
-the potential difference between two points is denoted as voltage
-
-the potential is the electrical potential energy per unit charge
-
-$$
-V_ab = \frac{w}{q}
-$$
-
-Voltage --> across
-Current --> through
-
-
-power = energy/time
-
-instantatneous power = p = dw/d = dw/dq \* dq/dt = v\*i
-energy -> power (iintegration)
-
-$$
-w(t) = \int 
-$$
-
-if voltage and current are both positive --> the positive charges move from a higher potential to a lower potential (in the direction of the current) (from + to -)
-
-The component absorbs power --> passive component
-
-\
-### Resistance and ohms law
-- ratio v(t)/i(t) at the same time instant t
-- = elements ability to resist the flow of electric current
-- wire like conductors 
-$$ R = \rho \cdot \frac{l}{A} \newline $$
-$$ \rho = resitivity $$
-$$ l = length\ of\ wire $$
-A = cross-sectional area
-
-conductance = reciprocal or resistance
-\[G\]  = S(iemens)
-$$ G = \frac{1}{R} = \frac{i}{v} $$
-most materials have non-linear resistance
-