Does anyone know what the laws of conservation are when dealing with resistors?

Well, I guess you can vaguely state if you have, for example, 2 resistors in series: then, in accordance with the law of conservation of energy, the voltage drop across each resistor (the energy used by each resistor) add up to the voltage (energy) supplied by the source.
This is only thin that really comes to mind. Whadya think?

You are correct in your understanding of the law of conservation of energy when it comes to resistors in series. In a series circuit, the total voltage supplied by the source is divided among the resistors. According to Ohm's Law, the voltage drop across each resistor is directly proportional to its resistance. Therefore, the sum of the voltage drops across all the resistors in a series circuit must equal the total voltage supplied by the source.

To calculate the voltage drop across each resistor in a series circuit, you need to know the total resistance of the circuit and the total voltage supplied by the source. The voltage drop across each resistor can be calculated using the formula:

V = IR

where V is the voltage drop, I is the current flowing through the resistor, and R is the resistance of the resistor.

If you know the resistance values of individual resistors in a series circuit, you can calculate the total resistance by summing up the individual resistances. The total voltage supplied by the source can be measured using a voltmeter or obtained from the specifications of the power supply.

Once you have the total resistance and the total voltage, you can use Ohm's Law to determine the voltage drop across each resistor.

Remember to be consistent with units when performing calculations, such as using volts for voltage, amps for current, and ohms for resistance. Additionally, it's important to use the correct mathematical conventions and proper algebraic manipulation to ensure accurate calculations.