50)A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance? Please show all work using this. (Actual values, equations, and drawings)
50)A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance? Please show all work using this. (Actual values, equations, and drawings)
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50)A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance?
Please show all work using this. (Actual values, equations, and drawings)
![Title: Understanding RC Circuits
**Text Transcription:**
1. **Given:**
- \( C = 25 \% \)
2. **Voltage across the capacitor:**
- \( V_C(t) = 0.632 V_{max} \)
3. **Question:**
- Find \( R \)?
4. **Formula for Time Constant (\( \tau \)):**
- \(\tau = R \cdot C \)
5. **Rearranged Formula:**
- \( \tau = \frac{\Delta t}{N} \)
6. **Solving for Resistance (\( R \)):**
- \( R = \frac{\tau}{C} = \frac{\Delta t}{N \cdot C} \)
7. **Substituting Values:**
- \( R = \frac{60s}{72 \cdot 25\% \cdot F} \)
8. **Final Expression for \( R \):**
- \( R = \)
**Diagram Explanation:**
- The diagram depicts a basic RC circuit. It includes:
- A resistor labeled \( R \).
- A capacitor labeled \( C \).
- A voltage source \( V \).
This diagram represents a typical RC charging circuit where the voltage across the capacitor over time is described by the equation \[ V_C(t) = V_{max}(1 - e^{-t/\tau}) \].
In this context, the goal is to determine the resistance \( R \) using the known capacitance and the time constant concept. The time constant \( \tau \) indicates how quickly the capacitor charges to approximately 63.2% of its maximum voltage (\( V_{max} \)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F183a4de2-60b8-4988-9fb9-0a70f8d6fd02%2F51eaae0b-38a6-45ed-8d9c-f021009c0812%2Fi7t92hv_processed.png&w=3840&q=75)
Transcribed Image Text:Title: Understanding RC Circuits
**Text Transcription:**
1. **Given:**
- \( C = 25 \% \)
2. **Voltage across the capacitor:**
- \( V_C(t) = 0.632 V_{max} \)
3. **Question:**
- Find \( R \)?
4. **Formula for Time Constant (\( \tau \)):**
- \(\tau = R \cdot C \)
5. **Rearranged Formula:**
- \( \tau = \frac{\Delta t}{N} \)
6. **Solving for Resistance (\( R \)):**
- \( R = \frac{\tau}{C} = \frac{\Delta t}{N \cdot C} \)
7. **Substituting Values:**
- \( R = \frac{60s}{72 \cdot 25\% \cdot F} \)
8. **Final Expression for \( R \):**
- \( R = \)
**Diagram Explanation:**
- The diagram depicts a basic RC circuit. It includes:
- A resistor labeled \( R \).
- A capacitor labeled \( C \).
- A voltage source \( V \).
This diagram represents a typical RC charging circuit where the voltage across the capacitor over time is described by the equation \[ V_C(t) = V_{max}(1 - e^{-t/\tau}) \].
In this context, the goal is to determine the resistance \( R \) using the known capacitance and the time constant concept. The time constant \( \tau \) indicates how quickly the capacitor charges to approximately 63.2% of its maximum voltage (\( V_{max} \)).
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