Question

Define current amplification factor α_DC and β_DC Obtain the relation between them. 

Answer 1

1. In the case of common emitter configuration, common base current gain or the current amplification factor (α_DC) is the ratio of the collector current to the emitter current. 
   α_DC = `"I"_"c"/"I"_"E"` ….(1)
2. Similarly, the common-emitter current gain of the current amplification factor (β_DC) is defined as the ratio of the collector current to the base current.
   β_DC = `"I"_"c"/"I"_"B"` ….(2)
3. Since, I_E = I_B + I_C 
   Dividing throughout by I_C,
   `("I"_"E")/("I"_"c") = "I"_"B"/"I"_"c" + 1`
   ∴ `1/alpha_"DC" = 1/beta_"DC" + 1` ....[From (1) and (2)]
   ∴ `alpha_"DC" = beta_"DC"/(1 + beta_"DC")`
   ∴ `beta_"DC" = alpha_"DC"/(1 - alpha_"DC")`