Resistive Circuits

Resistive Circuits

Circuit Topology:

Kirchhoff's Laws

Kirchhoff's current law: The sum of the currents into a node at any instant = 0.     A current directed away from the node is positive, a current going into the node is negative.          (notation wise (for calculating with this law only)).

Kirchhoff's volatage law: The sum of the voltages around any loop in a circuit is identically zero for all time.     Take into account polarity. Plus sign = from terminal + to -. Minus sign= from therminal - to +.

Connection of resistors is said to be in series when all the elements carry the same current. To identify them we look for two elements connected to a single node that has no other elements connected to it.

Voltage division:Voltage across a series combination of resistors is divided up between the individual resistors.Vn =             Rn                      * Vs                            Vn= voltage across the nth resistor          R1 + R2 + .... + RN

Rs (resistors in series) = R1 + R2 + ... + RN

Connection of resistors is said to be in parallel when the voltage across each element is the same.To identify a pair of parallel elements we look for two elements connected between a pair of nodes.

Rp= 1/R1 + 1/R2 + ...or Rp = R1*R2/ R1+R2 (only for 2 resistors in parallel)

Current divider:It divides the source current.i2 =       R1      * is        R1 + R2

Voltage sources connected in series = one single voltage source

V1 + V2

Current sources connected in parallel = one single current source

I1 + I2

We are not allowed to connect independent current sources in series. Series elements have the same current so that would make no sense.

We are not allowed to connect independent voltage sources in parallel. Parallel  elements have the same voltage so that would make no sense.

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