Recall that voltage is a measure of the "push" that moves electrons around a circuit. If you have a resistor in a circuit powered by a single 3 V battery and then simply add another 3 V battery, what do you expect will happen to the amount of current produced? Explain your answer.

To answer this question, let's break it down step by step:

1. Understanding Voltage and Current: Voltage (V) is the measure of the electrical potential difference, which provides the "push" that moves electrons through a circuit. Current (I) is the flow of electric charge, and it is directly proportional to the voltage applied across a resistor, according to Ohm's Law.

2. Ohm's Law: Ohm's Law states that $I = \frac{V}{R}$, where $I$ is the current, $V$ is the voltage, and $R$ is the resistance.

3. Initial Setup: Initially, you have a single 3 V battery powering a circuit with a resistor. The current produced in this setup can be calculated using Ohm's Law: $I_1 = \frac{3 \text{ V}}{R}$

4. Adding Another Battery: When you add another 3 V battery, the total voltage in the circuit depends on how the batteries are connected:

   • Series Connection: If the batteries are connected in series, their voltages add up. Therefore, the total voltage would be $3 \text{ V} + 3 \text{ V} = 6 \text{ V}$.
   • Parallel Connection: If the batteries are connected in parallel, the voltage remains the same as the voltage of one battery, which is 3 V.

5. Effect on Current:

   • Series Connection: With a total voltage of 6 V, the current can be recalculated using Ohm's Law: $I_2 = \frac{6 \text{ V}}{R}$ Since the voltage has doubled, the current will also double compared to the initial setup. Therefore, $I_2 = 2 \times I_1$.

   • Parallel Connection: With the voltage remaining at 3 V, the current will remain the same as in the initial setup: $I_2 = \frac{3 \text{ V}}{R} = I_1$

6. Conclusion: If the batteries are connected in series, the amount of current produced will double. If the batteries are connected in parallel, the amount of current produced will remain the same.