For a constant collector-emitter voltage of 8 V, the collector current of a transistor reached to the value of 6 mA from 4 mA, whereas base current changed from 20 μ A to 25 μ A value. If transistor is in active state, small signal current gain (current amplification factor) will be :

Solution

Physics sir · 3 steps

Small signal means changes: divide the change in collector current by the change in base current.

1. What small signal means. The small signal (ac) current gain compares how much I_C changes for a small change in I_B, with V_(CE) held constant. It uses the changes, not the values themselves.

   β_(ac) = ((Δ I_C)/(Δ I_B))_(V_(CE))

2. Find the changes. Δ I_C = 6 - 4 = 2 mA = 2 × 10⁻³ A. Δ I_B = 25 - 20 = 5 μA = 5 × 10⁻⁶ A.
3. So. β_(ac) = (2 × 10⁻³)/(5 × 10⁻⁶) = 400, which is option (b).

The idea to keep. Whenever a question says small signal or ac gain, take differences: Δ I_C / Δ I_B. A plain ratio like I_C / I_B gives the dc gain, which is a different quantity.

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