A : AC can be transmitted over long distances at high voltage without much power loss.
R : The average value of AC is defined over any half cycle.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statement, then mark (4)

Answer

To analyze the given statements A and R, we will evaluate each one step by step.

### Step 1: Understanding Assertion (A)
Assertion (A) states that "AC can be transmitted over long distances at high voltage without much power loss."

- This statement is true. The reason behind this is that when alternating current (AC) is transmitted at high voltages, the current flowing through the transmission lines is reduced. Power loss due to resistance in the wires is given by the formula:

\[ P_{\text{loss}} = I^2 R \]

where \( I \) is the current and \( R \) is the resistance. By increasing the voltage (and consequently reducing the current for a given power), the power loss can be minimized.

### Step 2: Understanding Reason (R)
Reason (R) states that "The average value of AC is defined over any half cycle."

- This statement is also true. The average value of an alternating current over a full cycle is zero because the positive and negative halves cancel each other out. Therefore, when calculating the average value, we typically consider only one half of the cycle (either the positive or negative half). For a sinusoidal waveform, the average value over a half cycle can be calculated as:

\[ V_{\text{avg}} = \frac{2V_0}{\pi} \]

where \( V_0 \) is the peak voltage.

### Step 3: Evaluating the Relationship Between A and R
While both statements A and R are true, we need to assess whether R correctly explains A.

- The assertion about AC transmission efficiency at high voltage is related to the reduction of current and power loss, while the reason given (average value of AC over half cycle) does not directly explain the assertion about power loss. Therefore, while both statements are true, R does not provide a valid explanation for A.

### Conclusion
- **Assertion (A)** is true.
- **Reason (R)** is true, but it does not explain A.

Thus, the correct answer is that both A and R are true, but R is not the correct explanation for A.