In series circuits, the voltage across each resistor can be determined by the following steps:
1. Calculate the total resistance (R_total) of the circuit by adding up the individual resistances (R1, R2, R3, etc.) connected in series.
2. Apply Ohm's Law: V = I * R, where V is the voltage, I is the current, and R is the resistance.
3. Since the resistors are connected in series, the current passing through each resistor is the same. Therefore, the voltage drop across each resistor can be calculated as V_resistor = I * R_resistor.
Now, let's go through the given options:
1. The resistor voltages multiplied together give the battery's voltage – This is incorrect. In a series circuit, the voltage drop across each resistor does not multiply together to give the battery's voltage.
2. The resistor voltages subtract to get the battery's voltage – This is also incorrect. Subtracting the voltage drops across each resistor will not give the battery's voltage.
3. The resistor voltages add to get the battery's voltage – This is the correct answer. In a series circuit, the voltage drops across each resistor add up to equal the voltage provided by the battery. Mathematically, it can be expressed as V_battery = V_resistor1 + V_resistor2 + V_resistor3 + ...
4. The resistor voltages are the same as the battery's voltage – This is incorrect. The battery's voltage is divided among the resistors in a series circuit, resulting in different voltage drops across each resistor.
5. The resistor voltages are smaller than the battery's – This is incorrect. The sum of the voltage drops across the resistors in a series circuit is equal to the battery's voltage.
6. There does not appear to be a pattern relating the voltages of the resistors and the battery – This is incorrect. There is a clear pattern in a series circuit where the voltage drops across the resistors add up to the battery's voltage.
7. The resistor voltages are larger than the battery's – This is incorrect. The sum of the voltage drops across the resistors in a series circuit is equal to the battery's voltage.
So, the correct answer is 3. The resistor voltages add to get the battery's voltage.