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Working with transistor switches

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Please check my work and if incorrect give me the correct answer

Please refer to the problem stated in the attached file.

(For the circuit shown below, find the values for Re and Rc to establish a collector current of 0.6 mA and a reverse-bias voltage on the collector-base junction of 2.2 V. Assume alpha is approximately equal to 1.)

My answer is given below:

We are to solve for Re

Vc=(10-4)-2.2=3.8
Ie=Ic/1=.6/1=.6
Rc=Vc/Ic=3.8/.6=6.333
Ve=ln.6=.51

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Collector voltage Vc = 10 - (4+2.2) = 3.8v

So, in order to maintain a current of 0.0006 ...

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