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In this problem, we are dealing with a camera flash circuit that involves a capacitor charging and discharging through different switches and resistors. Here’s a breakdown of the process and how we can approach Part B of the problem based on what you have provided so far.

**Part A:**  
The value of the capacitance \( C \) has already been calculated as \( 1.52 \times 10^{-2} \, \text{F} \), which is correct based on the time constant equation.

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### **Part B: Voltage at the time \( S_2 \) opens**

You are asked to find the voltage \( V_C \) across the capacitor at the time switch \( S_2 \) opens. To solve this, we can use the capacitor discharge equation:

\[
V_C(t) = V_0 \cdot e^{-\frac{t}{R_1 C}}
\]

Where:
- \( V_0 = 10.6 \, \text{V} \) (initial voltage across the capacitor),
- \( t = 2.94 \, \text{s} \) (time at which the voltage reaches 92% of the charge),
- \( R_1 = 76.5 \, \Omega \) (resistance in the charging circuit),
- \( C = 1.52 \times 10^{-2} \, \text{F} \) (capacitance of the capacitor).

We can calculate the voltage at the time \( t = 3.2 \times 10^{-2} \, \text{s} \) when \( S_2 \) closes and compare it with the voltage when \( S_2 \) opens.

Let me compute the value for you.The voltage across the capacitor at the time \( S_2 \) opens, \( t = 3.2 \times 10^{-2} \, \text{s} \), is approximately \( 10.3 \, \text{V} \) when rounded to three significant figures.

Would you like more details on the calculation, or have any questions about this result?

### Relative questions:
1. How does the time constant \( \tau = R \cdot C \) affect capacitor charging and discharging?
2. Why does the voltage across the capacitor not immediately drop to zero when switch \( S_1 \) opens?
3. What role do the switches \( S_1 \) and \( S_2 \) play in the overall circuit operation?
4. How can the total energy delivered to the resistor be calculated in this circuit?
5. How would the result change if a different resistor \( R_1 \) was used?

### Tip:
When solving problems involving capacitors, always check if the process is charging or discharging, as the equations for voltage differ.

What is the value of capacitance C and the voltage across the capacitor at the time switch S2 opens in a camera flash circuit?

Find the capacitance and voltage across a capacitor in a camera flash circuit using the exponential decay formula. Learn how the time constant (τ = RC) affects the charging and discharging of a capacitor. Ideal for undergraduate-level physics and electrical engineering students.

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