During current growth in an L-R circuit the time constant is the time in which the magnitude of current becomes

Options

A. `l_(0)`
B. `l_(0)//2`
C. `0.63l_(0)`
D. `0.37l_(0)`

Explanation

To solve the question regarding the time constant in an L-R circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the L-R Circuit**:
- An L-R circuit consists of an inductor (L) and a resistor (R) connected in series with a battery. When the circuit is closed, the current starts to grow from zero and approaches a maximum value.

2. **Identify the Maximum Current**:
- The maximum current (I₀) in the circuit can be determined using Ohm's law, which states that I₀ = V/R, where V is the voltage of the battery and R is the resistance.

3. **Write the Current Growth Equation**:
- The current (I) at any time (t) during the growth phase can be described by the equation:
\[ I(t) = I₀ (1 - e^{-Rt/L}) \]
- Here, \( e \) is the base of the natural logarithm, R is the resistance, L is the inductance, and t is time.

4. **Define the Time Constant (τ)**:
- The time constant (τ) for an L-R circuit is defined as:
\[ τ = \frac{L}{R} \]
- This time constant indicates how quickly the current reaches its maximum value.

5. **Determine the Current at Time Constant**:
- At time \( t = τ \):
\[ I(τ) = I₀ (1 - e^{-1}) \approx I₀ (1 - 0.3679) \approx I₀ (0.6321) \]
- This means that at the time constant, the current reaches approximately 63.2% of its maximum value.

6. **Conclusion**:
- Therefore, during the current growth in an L-R circuit, the time constant is the time in which the magnitude of the current becomes approximately 63.2% of the maximum current (I₀).

### Final Answer:
The time constant in an L-R circuit is the time in which the magnitude of the current becomes approximately 63.2% of the maximum current.

---