# Transistor Circuit question

I'm trying to solve a transistor problem, but I'm stuck on the I2. Is I2 equal to I0 ? The question is: The transistor circuit in Fig. 3.45 has β = 80 and VBE = 0.7 Find V0 and I0 . Answers : 12V, 600 mA.

My equations:

For $I_1$,

$-1+120 \mathrm{k} \cdot I_1 + V_{BE} = 0$.

Therefore, $I_1=2.5μA$.

For $I_3$,

$10\mathrm{k} \cdot I_3+20+10\mathrm{k} \cdot I_3 - 10\mathrm{k} \cdot I_2=0$.

$2\left(I_3\right )-I_2=-2\mathrm{mA}$

If $I_C=I_B \cdot \beta$, $I_B$ is equal to $I_1$, isn't it ?

However, I get $I_2=$ 0.8μA

The answer given is clearly wrong.

20 volts across a 10K resistor will give 2 mA, so $I_0$ can't possibly be 600 mA.

If we omit the transistor, the two 10K resistors form a voltage divider, dividing the 20 volt supply in half, making $V_0$ 10 volts.

The transistor will draw some current in parallel with the lower 10K, so $V_0$ must be less than 10 volts.

• In my head the answer seems to be 9V Vout and 900uA Iout. (The Thevenin impedance at the collector is 5K, w/10V. There is 200uA in the collector, a one volt drop from the 10V making Vout 9V. 9V/10K = 900uA. But that's just in my head, I didn't check it on paper. – John D Dec 28 '14 at 23:14
• @JohnD - I think you were spot on. – Floris Dec 28 '14 at 23:22

My approach:

Start with the transistor. You know there's 0.7 V Vbe, so 0.3 volts across the 120k resistor. That makes the base current 0.3/120k = 2.5 uA. Then the collector current is 80x that, so 0.2 mA.

Now we can draw a simpler circuit with a current source, two resistors and a voltage:

simulate this circuit – Schematic created using CircuitLab

Solving this circuit, we do indeed find that the voltage across R1 is 9 V; this makes the total current in R2 0.2 + 0.9 = 1.1 mA

The answer given (12V, 600 mA) is obviously wrong - 600 mA across the 10k resistor would develop a voltage of 60V, more than the voltage source is capable of providing. And given the two 10k resistors, you know that the voltage V0 can be at most 10V (if the transistor is fully turned off) - smaller if the transistor carries any current. 12V is never the right answer.