*Question E5B01:
What is the term for the time required for the capacitor in an RC circuit to be charged to 63.2% of the applied voltage or to discharge to 36.8% of its initial voltage?*  

*Correct Answer is  B: One time constant*  

### AI Response: (may contain errors)  

In an RC circuit, the term "one time constant" is used to describe the time required for a capacitor to charge to 63.2% of the applied voltage or to discharge to 36.8% of its initial voltage. This is a fundamental concept in understanding how capacitors charge and discharge over time.

### Explanation:

1. **Correct Answer: One time constant**
   - The time constant, denoted as $\tau$, is defined as the product of resistance ($R$) and capacitance ($C$) in the circuit:  
     $$\tau = R \times C$$
   - After one time constant ($\tau$), the voltage across the capacitor reaches approximately 63.2% of the difference between its initial value and its final value when charging, or it falls to 36.8% of its initial value when discharging.
   - This behavior is due to the exponential nature of the charging and discharging process in an RC circuit.

2. **Why the other choices are incorrect:**
   - **A: An exponential rate of one**
     - This choice is incorrect because "exponential rate of one" is not a standard term used to describe the time constant in an RC circuit.
   - **C: One exponential period**
     - This choice is incorrect because "one exponential period" is not a recognized term in the context of RC circuits. The concept of a "period" is more commonly associated with oscillations, not exponential charging or discharging.
   - **D: A time factor of one**
     - This choice is incorrect because "time factor of one" does not specifically describe the time constant in an RC circuit. The term "time constant" is the precise terminology used.

### Useful Formula:

- The voltage across a charging capacitor as a function of time $t$ is given by:  
  $$V(t) = V_0 \left(1 - e^{-t/\tau}\right)$$  
  where $V_0$ is the final voltage and $e$ is the base of the natural logarithm.

- The voltage across a discharging capacitor as a function of time $t$ is given by:  
  $$V(t) = V_0 e^{-t/\tau}$$  
  where $V_0$ is the initial voltage.

Understanding the concept of one time constant is crucial for analyzing the transient response of RC circuits.