For a transistor α and β are given as α = I_C/I_E and β = I_C/I_B. Then the correct relation between α and β will be :

Solution

Physics sir · 4 steps

Start from I_E = I_B + I_C, divide through 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.
2. Divide by IC. Dividing every term by I_C gives I_E/I_C = I_B/I_C + 1, which is 1/α = 1/β + 1.

   1/β = 1/α - 1 = (1 - α)/α ⇒ β = α/(1 - α)

3. Quick check. For a typical transistor α = 0.98, which gives β = 0.98/0.02 = 49. A large β from an α just below 1 is what you expect.
4. So. The correct relation is β = α/(1 - α), option (b).

The idea to keep. Every α and β relation comes from I_E = I_B + I_C. Remember β = α/(1-α) and its inverse α = β/(1+β), and check that α < 1 while β is large.

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