Final answer:
To determine the voltage across a resistor, the total resistance of the circuit must be calculated, which varies depending on whether the circuit is in series or parallel. The voltage across the battery is the same as the total voltage across all resistors in series or each resistor in parallel.
Step-by-step explanation:
To calculate the voltage across a resistor in a series circuit, we can use Ohm's Law and the rules for series circuits. For a series circuit, the total resistance (Rtotal) is the sum of the individual resistances (R1 + R2 + ... + Rn). Once we have the total resistance, we can use the formula V = I * R to find the voltage across any individual resistor (VR), where I is the current through the circuit and R is the resistance of the resistor in question.
In the case of a parallel circuit, the total resistance is calculated differently since resistors in parallel have the same voltage across them. The total resistance (Rtotal) can be found using the reciprocal formula 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn. The voltage across each parallel branch is equal to the voltage across the battery. Therefore, to find the voltage across any individual branch or combination of resistors in parallel, you use the voltage of the battery (Vbattery).
Knowing that the voltage across the battery must be equal to the total voltage across all other circuit components that are in series or parallel, we can use these relationships to solve for the unknown voltage across a resistor given the pertinent information about the circuit's configuration and the values of other voltages and resistances.