Assertion : In a common-emitter amplfier, the load resistnace of the output circuit is 1000 times the load resistance of the input circuit. If `alpha=0.98`, then voltage gain is `49xx10^(3)`.
Reason : `alpha=(beta)/(1-beta)` (symbols have their usual meanging).

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true but reason is not the correct explanation of assertion
C. If assertion is true but reason is false
D. If both assertion and reason are false.

Explanation

To solve the problem, we need to analyze the assertion and the reason given in the question step by step.

### Step 1: Understanding the Assertion
The assertion states that in a common-emitter amplifier, the load resistance of the output circuit (R0) is 1000 times the load resistance of the input circuit (Ri). This can be expressed mathematically as:
\[ R0 = 1000 \times Ri \]

### Step 2: Understanding the Relationship between α and β
The reason provided states that:
\[ \alpha = \frac{\beta}{1 - \beta} \]
Where:
- α (alpha) is the common base current gain.
- β (beta) is the common emitter current gain.

### Step 3: Finding β from α
Given that α = 0.98, we can rearrange the equation to find β:
\[ \beta = \alpha \times (1 - \beta) \]
Rearranging gives:
\[ \beta + \alpha \beta = \alpha \]
\[ \beta(1 + \alpha) = \alpha \]
\[ \beta = \frac{\alpha}{1 + \alpha} \]
Substituting α = 0.98:
\[ \beta = \frac{0.98}{1 + 0.98} = \frac{0.98}{1.98} \approx 0.4949 \]

### Step 4: Calculating the Voltage Gain
The voltage gain (Av) in a common-emitter amplifier can be expressed as:
\[ Av = \beta \times \frac{R0}{Ri} \]
Substituting the values we know:
- We have \( R0 = 1000 \times Ri \)
- Thus, \( \frac{R0}{Ri} = 1000 \)

Now substituting β and \( \frac{R0}{Ri} \):
\[ Av = 0.4949 \times 1000 \]
\[ Av \approx 494.9 \]

### Step 5: Conclusion about Voltage Gain
The assertion claims that the voltage gain is \( 49 \times 10^3 \), which is \( 49000 \). However, our calculation shows that the voltage gain is approximately \( 494.9 \), which does not match the assertion.

### Step 6: Evaluating the Reason
The reason provided is a correct relationship between α and β. However, it does not explain the assertion correctly since the calculated voltage gain does not match the assertion.

### Final Conclusion
- The assertion is **false** because the voltage gain calculated does not equal \( 49 \times 10^3 \).
- The reason is **true** as it correctly states the relationship between α and β.

Thus, the correct option is:
**If the assertion is true but the reason is false.**