An alternating current generator has an internal resistance `R_(g)` and an internal reactance `X_(g)`. It is used to supply power to a passive load consisting of a resistance `R_(g)` and a rectance `X_(L)`. For maximum power to be delivered from the generator to the load, the value of `X_(L)` is equal to

Options

A. zero
B. `X_(g)`
C. `-X_(g)`
D. `R_(g)`

Explanation

To solve the problem of finding the value of \( X_L \) for maximum power transfer from the alternating current generator to the load, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Components**:
- The generator has an internal resistance \( R_g \) and an internal reactance \( X_g \).
- The load consists of a resistance \( R_L \) (which is equal to \( R_g \)) and a reactance \( X_L \).

2. **Condition for Maximum Power Transfer**:
- For maximum power transfer in an AC circuit, the total reactance must be zero. This means that the reactance of the generator and the load must cancel each other out.

3. **Set Up the Equation**:
- The condition for maximum power transfer can be expressed as:
\[ X_g + X_L = 0 \]

4. **Solve for \( X_L \)**:
- Rearranging the equation gives:
\[ X_L = -X_g \]

5. **Conclusion**:
- Therefore, the value of \( X_L \) for maximum power transfer is equal to the negative of the internal reactance of the generator:
\[ X_L = -X_g \]

### Final Answer:
The value of \( X_L \) is \( -X_g \).

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