For a transistor amplifier power gain and voltage gain are `7.5 and 2.5` respectively. The value of the current gain will be

Options

A. `0.33`
B. `0.66`
C. `0.99`
D. `3`

Answer

To find the current gain of a transistor amplifier given the power gain and voltage gain, we can use the relationship between these gains.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Power Gain (Pg) is defined as the ratio of output power to input power.
- Voltage Gain (Av) is defined as the ratio of output voltage to input voltage.
- Current Gain (Ai) is defined as the ratio of output current to input current.

2. **Write the Formulas**:
- Power Gain (Pg) = Output Power / Input Power = (V_output * I_output) / (V_input * I_input)
- Voltage Gain (Av) = V_output / V_input
- Current Gain (Ai) = I_output / I_input

3. **Relate Power Gain, Voltage Gain, and Current Gain**:
- From the definition of power gain, we can express it as:
\[ Pg = Av \times Ai \]
- Rearranging this gives us:
\[ Ai = \frac{Pg}{Av} \]

4. **Substitute the Given Values**:
- Given:
- Power Gain (Pg) = 7.5
- Voltage Gain (Av) = 2.5
- Substitute these values into the rearranged formula:
\[ Ai = \frac{7.5}{2.5} \]

5. **Calculate Current Gain**:
- Performing the division:
\[ Ai = 3 \]

6. **Conclusion**:
- The value of the current gain is 3.

### Final Answer:
The current gain (Ai) is **3**.

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