An npn transistor operates as a common emitter amplifier with a power gain of 10⁶. The input circuit resistance is 100Ω and the output load resistance is 10 KΩ. The common emitter current gain 'β' will be ________. (Round off to the Nearest Integer).

Solution

Physics sir · 3 steps

Power gain is current gain squared times the resistance ratio, so peel off the ratio and take a root.

1. Build power gain. Voltage gain is β Rₒᵤₜ/Rᵢₙ and current gain is β. Power gain is their product, so β appears twice.

   A_P = β² Rₒᵤₜ/Rᵢₙ

2. Put in numbers. The resistance ratio is (10 × 10³ Ω)/(100 Ω) = 100. So 10⁶ = β² × 100, which gives β² = 10⁴.
3. So. β = √10⁴ = 100.

The common slip: 10000. Writing power gain as β Rₒᵤₜ/Rᵢₙ, which is really the voltage gain, gives β = 10⁴ instead of 100.

The idea to keep. For a CE amplifier, current gain is β, voltage gain is β Rₒᵤₜ/Rᵢₙ, and power gain is β² Rₒᵤₜ/Rᵢₙ. Check which gain the question gives before you solve.

Answer from the NTA final answer key. Solution by PrepWiser.