Electrical Circuits

• Light propagation is simply described by a ray which indicates a path of light energy.
• Voltage is the enery per unit charge created by charge seperation.

v=dw/dq  ---->  v= The voltages in volt (V)

                               w= The energy in joules (J)

                               q= The charge in coulombs(C)

• Current is the rate of charge flow.

i= dq/dt ----> i= The current in amperes (A)

                          q= The charge in coulombs (C )

                           t= The time in seconds (s)

• Power is the energy per unit of time.

p= dw/dt ----> p= The power in watts (W)

                             w= The energy in joules (J)

                              t= The energy in Time (s)

p=dw/dt=(dw/dq)(dq/dt)=vi  ----> p= The power in watts (W)

                                                                      w=The energy in joules (J)

                                                                       t=Time in seconds (s)

• p>0 ---> means that the power is being absorbed or dissipated by circuit element.
• p<0 ---> means that the power is being generated or delievered by the circuit element.

• When the current is flowing the directionof voltage drop, i.e, from + to -  --->p=vi.
• Substitute the value for the voltage and current in the power equation. If p>o  --->absorbed or dissipated. If p<0 ---> delivered or generated.
• A circuit schematic is a diagram representing a set of interconnected circuit elements: voltage sources, current sources, and resistors.
• Each element in the schematic is modeled and presented by a symbol.
• Lines connecting the symbols in the schematic can be considered as wires with zero resistance.
• An Ideal basic circuit element is a two terminal componet that can not be subdidvided and is described mathematically in terms of its voltage and current.
• Passive sign convention: whenever the reference direction of the current is in the direction of the voltage drop across its terminals, use a positive sign in any expression relating voltage to the current. Otherwise, use a negative sign.
• There are 5 idea basic circuit elements:

1. Voltage source
2. Current source
3. Resistor
4. Capacitor
5. Inductor

• (Vs)(+,-): Ideal independent voltage source
• (Is)(->): Ideal independent current source
• (Vs=uVx)(+,-): Ideal dependent voltage-controlled voltage source
• (Vs=pIx)(+,-): Ideal dependent current-controlled voltage source
• (Is=aVx)(->): Ideal dependent voltage-controlled current source
• (Is=bIx)(->): Ideal dependent current-controlled current source

*(u,p,a,b all stand for greek symbols)

The R-L Circuit

An electrical circuit whose total resistance is R ohms and whose self-inductance, shown schematically as a coil, is L henries ( hence the name " R-L circuit").  There is also a switch whose terminals at a and b can be closed to connect to a constant electrical source of V volts.