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