## Electrical Engineering 2 – Ways to Solve Linear Circuits

Power Dissipation
Depending on specific courses, positive power dissipation may mean different things. For this site’s purposes negative power dissipation means that the device is supplying power. This means that a battery would have negative power. This is because current flows from – to + inside a battery. Resistors will always have a positive power dissipation. Energy is conserved so if you sum all the power dissipations in a circuit the result should be 0W.

Kirchhoff’s Current Law(KCL)
This states that all current entering a node must be leaving a node. This is accomplished by having currents entering a node be positive while those leaving a node be negative. What sign you label the diagram does not matter as the solved value will just be (-) if you labeled the opposite way. Since this is a double negative you will still achieve the same answer. A node is where two or more wires meet. Such examples of KCL are where a battery and reistor meet as well as where 3 resistors meet.

Kirchoff’s Voltage Law(KVL)
This law states that all voltages around a closed loop must be equal to 0. This can be thought of intuitively by looking at a very simple circuit of just a battery and a resistor. The voltage supplied by the battery must be fully dissipated by the resistor. This same logic applies to complicated loops. Be careful to pay attention to the signs.

I repeat KVL is around loops
KCL is at nodes

Thevenin and Norton Equivalents
Creating Thevenin and Norton equivalents are ways of condensing complex linear circuits into one resistor in series with a voltage source(Thevenin Equivalent) or one resistor in parallel with a current source(Norton Equivalent). A “black box” can be represented by both of these models. Converting a circuit into these models is known as “source transformation”.

Voltage Divider
A voltage divider is formed when two or more resistors are in series. The voltage drop across R1 can be represented as VR1 = (R1)(R1 + Rn)(VIN) where Rn is the sum of the rest of the resistances in the series chain excluding R1.
Current Divider
A current divider is formed when two or more resistors are in parallel. The current through R1 can be represented as IR1 = (Rn)(R1+Rn)(IIN) where Rn is the equivalent resistance of all the resistors in parallel excluding R1.
Superposition
When there are multiple voltage or current sources in a circuit you solve for the voltage and current at each node with only one source in mind and then add all the values together in the end to get the actual value. If you keep your sign conventions constant, values may come out negative. This is what you want because one current can oppose another and in the circuit they may cancel each other out. When removing a voltage source from the circuit you short the nodes it as if a piece of wire was there. When removing a current source you keep the nodes open as if nothing was connecting the nodes.