Cheat Sheet : Voltage Divider, Kirchhoff’s laws and combination circuit

Voltage Divider:

The equation of the voltage divider for multiples resistors as long as the resistors are in series :

$Vx=Vin*\cfrac{Rx}{Rx+Rn1+Rn2+\dots}$

where Vx is the voltage across the resistor Rx and Vin is the voltage across all resistors in series.

Kirchhoff’s voltage law:

Kirchhoff’s voltage law or loop (mesh) rule states that the sum of voltages in a closed loop will be equal to 0.

$\sum\limits_{i=1}^n V_{i}=0$

where n is the total numbers of voltage in the loop. Voltage gain in a loop (voltage source are an example) will have a positive value and voltage drop will have a negative value.

Kirchhoff’s current law:

Kirchhoff’s current law or nodal rule states that the sums of currents flowing into any node or junction in a circuit will be equal to 0. In others words, the sums of current flowing into the node and out of the node will be equal.

$\sum\limits_{i=1}^n I_{i}=0$

where n is the total numbers of current flowing into and out of the node. Current flowing into the node will have a positive value and current flowing out of the node will have a negative value.

Combination circuit:

You can find below a small guide to solve a combination circuit without using complex algebra. Most of the times, you should be able to solve combination circuit with this method.

Verify if you can use Ohm’s law anywhere to find some information. If you can, use it to find unknown voltages, currents or resistances. Otherwise, move to step 2.
Simplify the circuit until you get a simple circuits like a series, parallel or voltage divider circuit. You can simplify it multiples times to reach a simple circuits.
Use Ohm’s law or voltage divider formula to find unknown voltages, currents or resistances.
De-simplify the circuit (one times if you did multiples simplification) and add the information you found like currents, voltages and resistances.
Use Ohm’s law to find the missing information in the de-simplify circuits.
If the circuit is still not completely de-simplified, restart from step 4 until you get the original circuit.
Use Ohm’s law and Power law if needed to find the missing information in the original circuit.