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The ratio of the short circuit current gain of a current amplifier (Ai) to the open circuit voltage gain of a voltage amplifier (AV), given that both amplifiers have the same value of the input resistance (Ri) and output resistance (R0), is
  • a)
    Ri
  • b)
     Ro
  • c)
    Ri / R0
  • d)
    Ro / Ri
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The ratio of the short circuit current gain of a current amplifier (Ai...
It is a standard mathematical relation.
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Understanding Amplifier Parameters
In electrical engineering, amplifiers can be categorized based on their functionality, primarily into current amplifiers and voltage amplifiers. The given problem compares the short circuit current gain (Ai) of a current amplifier with the open circuit voltage gain (AV) of a voltage amplifier.

Short Circuit Current Gain (Ai)
- The short circuit current gain (Ai) is defined as the ratio of the output current (Io) to the input current (Ii) when the output is shorted.
- Mathematically, it can be expressed as:
Ai = Io / Ii

Open Circuit Voltage Gain (AV)
- The open circuit voltage gain (AV) measures the ratio of the output voltage (Vo) to the input voltage (Vi) under open-circuit conditions.
- This is given by:
AV = Vo / Vi

Relationship Between Gains
Given that both amplifiers have the same input resistance (Ri) and output resistance (Ro), the relationship between Ai and AV can be analyzed as follows:
- The input voltage (Vi) can be expressed in terms of input current (Ii) and input resistance (Ri):
Vi = Ii * Ri
- The output voltage (Vo) for the voltage amplifier can be expressed in terms of output current (Io) and output resistance (Ro):
Vo = Io * Ro
- Substituting these into the expressions for gains leads to:
AV = (Io * Ro) / (Ii * Ri)
- Rearranging gives:
AV = (Ro / Ri) * Ai
- This shows that the ratio of Ai to AV is:
Ai / AV = Ri / Ro

Conclusion
Thus, the ratio of the short circuit current gain of the current amplifier to the open circuit voltage gain of the voltage amplifier is:
**Ai / AV = Ri / Ro**,
which corresponds to option **C**: Ri / Ro.
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The ratio of the short circuit current gain of a current amplifier (Ai...
Ri/Ro correct
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The ratio of the short circuit current gain of a current amplifier (Ai) to the open circuit voltage gain of a voltage amplifier (AV), given that both amplifiers have the same value of the input resistance (Ri) and output resistance (R0), isa)Rib)Roc)Ri/ R0d)Ro/ RiCorrect answer is option 'C'. Can you explain this answer?
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