Question

For a common emitter amplifier. DC current gain is $100$. If the base current is $20\,\mu A$, calculate the collector and emitter current.

Answer 1

****Hint: The collector current and the emitter current can be determined by using two formulas, the current gain formula and the emitter current formula. By using the current gain formula, the collector current is determined. And by using the emitter current formula, the emitter current is determined.

Useful formula:
The current gain of the common emitter amplifier is given by,
$\beta = \dfrac{{{I_C}}}{{{I_B}}}$
Where, $\beta$ is the current gain, ${I_C}$ is the collector current and ${I_B}$ is the base current.
The emitter current of the common emitter amplifier is given by,
${I_E} = {I_C} + {I_B}$
Where, ${I_E}$ is the emitter current, ${I_C}$ is the collector current and ${I_B}$ is the base current.

Complete step by step solution:
Given that,
The current gain, $\beta = 100$
The base current, ${I_B} = 20\,\mu A$
Now, by using the current gain formula,
The current gain of the common emitter amplifier is given by,
$\beta = \dfrac{{{I_C}}}{{{I_B}}}\,.....................\left( 1 \right)$
By substituting the current gain and the base current value in the above equation (1), then the equation (1) is written as,
$100 = \dfrac{{{I_C}}}{{20}}$
By keeping the collector current in one side and the other terms in other side, then the above equation is written as,
${I_C} = 100 \times 20$
On multiplying the above equation, then the above equation is written as,
${I_C} = 2000\,\mu A$
Now, by using the emitter current formula,
The emitter current of the common emitter amplifier is given by,
${I_E} = {I_C} + {I_B}\,.....................\left( 2 \right)$
By substituting the collector current and the base current in the above equation (2), then the above equation (2) is written as,
${I_E} = 2000 + 20$
By adding the above equation, then the above equation is written as,
${I_E} = 2020\,\mu A$
Thus, the collector current is ${I_C} = 2000\,\mu A$ and the emitter current is ${I_E} = 2020\,\mu A$.

Note: Most of the amplifiers use the common emitter circuit configuration because it offers both the current and the voltage gain resulting in the higher power gain than in the common base emitter configuration. The other consideration is that the input resistance is high and of the order of low resistance.