DC Analysis

Important

DC solution to a circuit is a solution consisting entirely of constant signals

Methods of solving

Kirchoff Laws

Device equations

Nodal method

Label all nodes denoting electric potentials
Label all currents flowing into the elements
Solving, we can find that $e_{6} = 0$ so we can redraw the circuit like so

Which is extremely easy to solve

Superposition rule

Important

A solution to a linear circuit with $N$ independent sources is a sum of all solutions to $N$ circuits with only one source connected at a time

Voltage source becomes short-circuit,current source becomes open-circuit

Example

Circuit 1: i_{1} = \frac{E_{1}}{R_{1} + R_{2}} and u_{1} = i_{1} R_{2} = E_{1} \frac{R_{2}}{R_{1} + R_{2}}

Circuit 2: i_{2} = J \frac{R_{1}}{R_{1} + R_{2}} and U_{2} = - J \frac{R_{1} R_{2}}{R_{1} + R_{2}}

Circuit 3: i_{3} = \frac{E_{2}}{R_{1} + R_{2}} and U_{3} = E_{2} \frac{R_{2}}{R_{1} + R_{2}}

Solving by inspection

Introduce unknown variables
Determine number of voltages and currents by KVL, KCL and device equations
Setup equations from KCL, KVL and device equations
If number of equations is too low, repeat from step 1
Solve

Current Divider Formula (CDF)

{\begin{cases} KCL: i_{2} = J - i_{1} \\ Ohm: u_{2} = R_{2} (J - i_{1}) \\ KVL: R_{1} i_{1} = R_{2} (J - i_{1}) \end{cases}

$i_{1} = J \frac{R_{2}}{R_{1} + R_{2}} and i_{2} = J \frac{R_{1}}{R_{1} + R_{2}}$ $

Voltage Divider Formula (VDF)

u_{1} = E \frac{R_{1}}{R_{1} + R_{2}}

u_{2} = E \frac{R_{2}}{R_{1} + R_{2}}