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The image shows a question regarding the rate of change of voltage across a capacitor as it is being charged. Specifically, you are tasked with estimating the rate of change of voltage at \( t = 20 \, \text{s} \) using the provided graph.

### Key Information:
- The graph plots voltage \( V(t) \) (in volts) as a function of time \( t \) (in seconds).
- You are asked to estimate the derivative \( \frac{dV}{dt} \) at \( t = 20 \, \text{s} \), which represents the slope of the tangent to the curve at that time.
- The provided incorrect answer in the image is \( \frac{dV}{dt} = 2 \), which is marked as wrong.

### Solution Steps:
1. **Visualize the slope at \( t = 20 \, \text{s} \):**
   At \( t = 20 \, \text{s} \), look at the steepness of the graph at that point. The slope \( \frac{dV}{dt} \) is the change in voltage over the change in time around that point.

2. **Use a linear approximation:**
   Find two points close to \( t = 20 \, \text{s} \) on the graph and estimate the slope by calculating:
   \[
   \frac{dV}{dt} \approx \frac{V(t_2) - V(t_1)}{t_2 - t_1}
   \]
   where \( t_1 \) and \( t_2 \) are times around 20 seconds.

Would you like me to walk you through these steps in more detail? 

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Here are some related questions to deepen your understanding:
1. How does the rate of change of voltage across a capacitor relate to the charging process?
2. What physical phenomena govern the shape of the voltage curve when charging a capacitor?
3. How is the rate of change of voltage at any time connected to the capacitance and resistance in a circuit (in terms of time constant)?
4. What are the units of \( \frac{dV}{dt} \) in this context, and how do they reflect the slope of the graph?
5. What would the voltage-time graph look like if the capacitor were discharged?

**Tip:** To improve accuracy when estimating slopes from graphs, pick points as close as possible to the target point for better approximation of the derivative.

Estimate the rate of change of voltage at t = 20 s using the provided graph of voltage across a capacitor as a function of time while the capacitor is being charged.

Learn how to estimate the rate of change of voltage across a capacitor at t = 20 seconds using the graph provided. This problem involves concepts of differentiation, linear approximation, and the slope of a tangent line. Suitable for students in Grades 10-12.

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