The correct relation between α (ratio of collector current to emitter current) and β (ratio of collector current to base current) of a transistor is :

Solution

Physics sir · 4 steps

Start from I_E = I_B + I_C, divide every term by I_C, and the relation drops out in one line.

1. Current balance. Charge entering the emitter leaves through either the base or the collector, so I_E = I_B + I_C. By definition α = I_C/I_E and β = I_C/I_B.
2. Divide by IC. Dividing I_E = I_B + I_C by I_C gives I_E/I_C = I_B/I_C + 1, that is 1/α = 1/β + 1 = (1+β)/β.

   α = β/(1+β) β = α/(1-α)

3. Sanity check. A typical transistor has β = 100, which gives α = 100/101 ≈ 0.99. That is just below 1, as it must be, because I_C is always a little less than I_E.
4. So. The correct relation is α = β/(1+β), option (c).

The idea to keep. For any α, β question, go back to I_E = I_B + I_C and divide by I_C. Then check with β ≈ 100: α must come out just under 1.

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