Final answer:
To calculate the potential difference across resistor 1 in the series circuit, sum the resistances, calculate the total current with Ohm's Law using the battery voltage, then calculate the voltage across the first resistor by multiplying the total current by r1's resistance.
Step-by-step explanation:
The question addresses a situation where two resistors, r1 (40 Ω) and r2 (70 Ω), are connected in series to a 9.0 V battery. To find the potential difference across resistor 1 (r1), we need to use Ohm's Law and the concept of series circuits.
In a series circuit, the total resistance (Rt) is the sum of the individual resistances. Thus, Rt = r1 + r2 = 40 Ω + 70 Ω = 110 Ω. The total current (It) through the circuit can be found using Ohm's Law, V = ItRt, where V is the battery voltage. So It = V / Rt = 9.0 V / 110 Ω.
Once we have the total current, the potential difference across r1 is found as Vr1 = Itr1. This calculation gives us the voltage drop across resistor 1, which answers the question posed.