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 reactance `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, we need to determine the value of the load reactance \( X_L \) for maximum power transfer from the generator to the load.

### Step-by-Step Solution:

1. **Understanding Maximum Power Transfer**:
For maximum power to be delivered from an AC generator to a load, the total reactance in the circuit must be zero. This means that the reactance of the load must cancel out the reactance of the generator.

2. **Identify Given Parameters**:
- Internal resistance of the generator: \( R_g \)
- Internal reactance of the generator: \( X_g \)
- Load resistance: \( R_L \) (not directly relevant for this calculation)
- Load reactance: \( X_L \)

3. **Setting Up the Condition for Maximum Power**:
The condition for maximum power transfer is that the total reactance \( X_{total} \) in the circuit must equal zero. This can be expressed mathematically as:
\[ X_g + X_L = 0 \]

4. **Solving for Load Reactance**:
Rearranging the equation gives us:
\[ X_L = -X_g \]
This means that the load reactance \( X_L \) must be equal to the negative of the generator's internal reactance \( X_g \).

5. **Conclusion**:
Therefore, for maximum power to be delivered from the generator to the load, the value of \( X_L \) should be:
\[ X_L = -X_g \]

### Final Answer:
The value of \( X_L \) for maximum power transfer is \( -X_g \).

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