The time required for a current to attain the maximum value in a d.c circuit containing L and R depends upon :

Options

A. R only
B. L only
C. L/R
D. none of these

Answer

To solve the question regarding the time required for a current to attain the maximum value in a DC circuit containing an inductor (L) and a resistor (R), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Circuit**:
- We have a DC circuit that consists of a resistor (R) and an inductor (L) connected in series. When the circuit is closed, the current starts from zero and gradually increases until it reaches a maximum steady-state value.

2. **Current Growth Formula**:
- The growth of current in an RL circuit can be described by the formula:
\[ I(t) = I_0 (1 - e^{-\frac{R}{L}t}) \]
where \( I(t) \) is the current at time \( t \), \( I_0 \) is the maximum current (steady-state value), \( R \) is the resistance, \( L \) is the inductance, and \( e \) is the base of the natural logarithm.

3. **Finding the Maximum Current**:
- The maximum current \( I_0 \) is attained as \( t \) approaches infinity. This is because the exponential term \( e^{-\frac{R}{L}t} \) approaches zero as \( t \) increases.

4. **Setting the Equation for Maximum Current**:
- To find the time when the current reaches its maximum value, we set:
\[ I(t) = I_0 \]
Substituting this into our growth formula gives:
\[ I_0 = I_0 (1 - e^{-\frac{R}{L}t}) \]
Dividing both sides by \( I_0 \) (assuming \( I_0 \neq 0 \)):
\[ 1 = 1 - e^{-\frac{R}{L}t} \]
This simplifies to:
\[ e^{-\frac{R}{L}t} = 0 \]

5. **Conclusion on Time**:
- The equation \( e^{-\frac{R}{L}t} = 0 \) implies that \( t \) must approach infinity for the current to reach its maximum value. Therefore, the time required for the current to attain the maximum value does not depend on the values of \( R \) or \( L \); rather, it is infinite.

6. **Final Answer**:
- The time required for the current to attain the maximum value in a DC circuit containing an inductor (L) and a resistor (R) is infinite, and thus it does not depend on either \( R \) or \( L \).