Simple DC Circuit Analysis with Transistor

In summary, the conversation is about solving a circuit problem involving clockwise loops and using Kirchhoff's Voltage Law (KVL). The attempts at a solution involve assigning currents to each loop and using Ohm's Law to find the values of each current. However, the given values for Vo and Io do not follow Ohm's Law and the incorrect answers lead to further discussion and confusion. Eventually, it is discovered that the correct answer is 9 * 10^-4 A for Io, as confirmed by the author's errata for Alexander's Fundamentals of Electric Circuits.
  • #1
Dan97
6
0

Homework Statement


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Homework Equations



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The Attempt at a Solution


All loops are clockwise;

KVL Loop around 1V, 120kOhm and VBE (I1 is assigned to the loop):

-1V + 120kOhm * I1 + VBE = 0
I1 = IB = 0.3V / 120kOhm = 2.5 * 10-6 A;

Loop around 10kOhm, vCE (I2 is assigned to the loop);

KVL Loop around 10kOhm, vo, and 20V (I3 is assigned to the loop):

10kOhm * I3 + 20V - vo = 0
vo = 10kOhm * (I2 - I3)
10kOhm * I3 +20V + (I3 - I2) * 10kOhm = 0 (1);

At the node connecting the collector part of the transistor, Io and 10kOhm:

I3 + (I2 - I3) + IC = 0
since Io = I2 - I3

IC = B * IB = 80 * 2.5 * 10-6 = 2 * 10-4 A

I2 = -2 * 10-4 A (2);

Subbing (2) into (1):

10kOhm * I3 +20V + (I3 + 2 * 10-4 A) * 10kOhm = 0

20kOhm * I3 = - 20V - 2 * 10-4 A * 10kOhm

I3 = -22 / 20k A = -1.1 * 10-3

I2 - I3 = 9 * 10 -4 A ! = 6 * 10 -4 WRONG

And I've been stuck redoing the same equations for a day now... Would be nice if someone could help find the problem in my "solution" so I can finally move on haha.
 
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  • #2
Hi Dan97. :welcome:

clockwise Σ of voltages: vo + 10k × I3 + –20 = 0

EDITED
 
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  • #3
Hi @NascentOxygen ,

If loop 3 is clockwise, and it goes through the passive configuration, then it should be +20V - vo +I3 * 10kOhm?

I'm not sure what you're trying to say...
 
  • #4
Dan97 said:
Hi @NascentOxygen ,

If loop 3 is clockwise, and it goes through the passive configuration, then it should be +20V - vo +I3 * 10kOhm?

I'm not sure what you're trying to say...
The given values of Vo and Io do not follow Ohm's law.
I am also getting Io=9*10-4 A.
 
  • #5
Hi @cnh1995 ,

Could you show your working (if it's not too much of a hassle)? :)
 
  • #6
Dan97 said:
Hi @NascentOxygen ,

If loop 3 is clockwise, and it goes through the passive configuration, then it should be +20V - vo +I3 * 10kOhm?

I'm not sure what you're trying to say...
Sorry, typo. Corrected.

Following your path, it will be +20V - vo – I3 * 10k = 0

Current through a resistor (in fact, through any element that's not a source) flows from its more-positive end to its less-positive end. If you draw an arrow showing this PD across the resistor, the arrow's tail is at the less-positive end and the arrow head is at the more-positive end.
 
  • #7
@NascentOxygen ,

Why would it be - I3 * 10kOhm? Isn't that breaking Ohm's Law?
 
  • #8
The given answers are 12V and 600uA, which are incorrect. They don't follow Ohm's law.
Dan97 said:
Hi @cnh1995 ,

Could you show your working (if it's not too much of a hassle)? :)
Collector current Ic=2x10-4A.

Using KVL you can write,
104*Io=20-104*(Io+2*10-4).

Solving this for Io, we get Io=9×10-4 A.
 
  • #9
@cnh1995 ,

Oh actually I've made a big fuss for nothing! I've just look at the author's errata and the answer is indeed 9 * 10 -4!

1zlddt0.png
 
  • #10
what book is this anyway?
 
  • #11
e0ne199 said:
what book is this anyway?

Alexander's Fundamentals of Electric Circuits
 

FAQ: Simple DC Circuit Analysis with Transistor

1. What is a transistor and how does it function in a DC circuit?

A transistor is a semiconductor device that can amplify or switch electronic signals. In a DC circuit, a transistor acts as a switch, controlling the flow of current through the circuit.

2. How do I determine the voltage and current in a simple DC circuit with a transistor?

To determine the voltage and current in a simple DC circuit with a transistor, you will need to use Ohm's Law and Kirchhoff's Laws. First, calculate the total resistance in the circuit using Ohm's Law. Then, use Kirchhoff's Laws to analyze the voltage and current at each point in the circuit, taking into account the voltage drop across the transistor.

3. What is the difference between a NPN and PNP transistor?

A NPN transistor has a layer of N-type semiconductor sandwiched between two layers of P-type semiconductor, while a PNP transistor has a layer of P-type semiconductor sandwiched between two layers of N-type semiconductor. This difference in composition affects the direction of current flow in the transistor.

4. How do I choose the right transistor for my DC circuit?

When choosing a transistor for a DC circuit, you will need to consider factors such as the maximum voltage and current ratings, the gain or amplification factor, and the type of transistor (NPN or PNP). It is also important to ensure that the transistor can handle the power requirements of your circuit.

5. Can I use a transistor in an AC circuit?

Yes, a transistor can be used in an AC circuit. However, the analysis and calculations will be more complex since AC circuits involve alternating current and varying voltages. The transistor will still function as a switch or amplifier, but the calculations will need to take into account the frequency and phase of the AC signal.

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