A resistor, capacitor, switch, and ideal battery are in series. Originally the capacitor is uncharged. The switch is then closed, allowing current of flow
While the current is flowing, the potential difference across the resistor is

Options

A. Increasing
B. Decreasing
C. Fixed
D. First increase then decreases

Answer

To solve the problem, we need to analyze the behavior of the circuit components when the switch is closed. Here’s a step-by-step breakdown:

### Step 1: Understanding the Circuit
We have a series circuit consisting of a resistor (R), a capacitor (C), a switch, and an ideal battery (V). Initially, the capacitor is uncharged, meaning there is no voltage across it.

**Hint:** Remember that in a series circuit, the same current flows through all components.

### Step 2: Closing the Switch
When the switch is closed, current starts to flow from the battery through the resistor and into the capacitor. The current (I) at this moment can be calculated using Ohm's law, but since the capacitor is uncharged, the initial current is at its maximum.

**Hint:** Think about how the capacitor behaves when it starts charging.

### Step 3: Analyzing the Potential Difference Across the Resistor
The potential difference (V_R) across the resistor can be expressed using Ohm's law:
\[ V_R = I \cdot R \]
Since the capacitor is initially uncharged, the entire voltage from the battery appears across the resistor at the moment the switch is closed.

**Hint:** Consider that as the capacitor charges, the current will change.

### Step 4: Charging of the Capacitor
As time progresses, the capacitor begins to charge, which means the voltage across the capacitor (V_C) increases. The voltage across the resistor will decrease as the capacitor charges because the total voltage from the battery must equal the sum of the voltage across the resistor and the capacitor:
\[ V = V_R + V_C \]

**Hint:** Recall that the sum of the potential differences in a series circuit equals the total voltage supplied by the battery.

### Step 5: Conclusion on the Potential Difference Across the Resistor
Since the voltage across the capacitor increases as it charges, the voltage across the resistor must decrease. Therefore, the potential difference across the resistor (V_R) is decreasing over time.

**Final Answer:** The potential difference across the resistor is **decreasing**.