Solve for Vo in Transistor Circuit

[Tekneek]

Homework Statement

So I am supposed to find Vo in this circuit. Given, Vb-Ve=0.7, ic=100ib, ie=ic+ib

The Attempt at a Solution

In order to solve for Vout i did KVL for the two loops:

Loop 1 (left side, clockwise):

Vb-Ve-ie(416)+2-ib(10*10³)=0
0.7-ic(416)-ib(416)+2-ib(10*10³)=0
0.7-ib(100)(416)-ib(416)+2-ib(10*10³)=0
2.7-52016ib=0
ib=5.19*10^-5A

ic=5.19mA
ie=ic+ib=5.2mA
Ve=ie(416)=2.18V (this one i am not sure)

Loop 2 (Right side, anti-clockwise)

10-ic(2*10³)-Vo-Ve-ie(416)=0
Subbing in everything i get
Vo=4.7V

But the answer is supposed to be 5 Volts, i am not sure where i made a mistake.

 

[phyzguy]

The 2V and the 0.7V in the left hand loop are in opposite directions, so they should subtract, not add, so you should get 1.3-52016*Ib=0.

 

[Tekneek]

The 2V and the 0.7V in the left hand loop are in opposite directions, so they should subtract, not add, so you should get 1.3-52016*Ib=0.

I still don't get the right answer, this time around i get 7.87

 

[phyzguy]

You've made another mistake in the right hand loop, but you don't really need that. With what I gave you, you should get Ib = 25μA. Ic = 100* Ib = 2.5 mA. Vout = 10.0 - 2.5mA * 2.0 kΩ = 5.0V

 

[rezeew]

Great job on using KVL to solve for Vo in this transistor circuit! Your approach looks correct, but there are a few small mistakes that may have led to the incorrect answer.

Firstly, in your first loop, when you substitute in the values for Vb and Ve, it should be 0.7V-ib(416)=0 instead of 0.7-ib(416)+2=0. This is because the voltage drop across the base-emitter junction is 0.7V, so you should only include that value and not the 2V in your equation.

Secondly, in your second loop, when you substitute in the values for Ve and ie, it should be -Ve-ie(416)=0 instead of -Ve-ie(416)-ie(416)=0. This is because the current flowing through the base-emitter junction is the same as the current flowing through the resistor, so you only need to include it once in your equation.

Finally, when you solve for Vo, you should get Vo=5V instead of 4.7V. This is because when you substitute in all the values, you should get Vo=5V instead of 4.7V. This may have been a calculation error or a rounding error.

Overall, your approach was correct, but just be sure to double check your equations and values to avoid small mistakes that can affect the final answer. Keep up the good work!