In common emitter mode of transistor, the d.c. current gain is $20$, the emitter current is $7$ mA. The collector current is

Given the d.c. current gain in common emitter mode, $\beta = 20$

Emitter current, $I_E = 7$ mA

The relation between current gain in common base mode ($\alpha$) and common emitter mode ($\beta$) is given by:

$\alpha = \dfrac{\beta}{1 + \beta}$

Substituting the value of $\beta$:

$\alpha = \dfrac{20}{1 + 20} = \dfrac{20}{21}$

We also know that $\alpha = \dfrac{I_C}{I_E}$, where $I_C$ is the collector current.

Therefore, $I_C = \alpha I_E$

Substituting the values:

$I_C = \dfrac{20}{21} \times 7 = \dfrac{20}{3}$ mA

Answer: $\dfrac{20}{3}$ mA