Thevenin/Kirchhoff('s) laws.

Question as above.

My working:
Break each loop into its own current:
$-12+2000i_1+4000(i_1-i_2)=0$
$500i_2-4000(i_2-i_1)=0$
Simultaneous equations, solve:
$-2500i_2=-24$
Solutions:
$9.6 \times 10^{-3}=i_2$ and $8.4 \times 10^{-3}=i_1$

Is this right? If it is, how do I do part (d)? Thevenin's theorem is for working out the simplified circuit of Figure 5, why would I use it to work out the short-circuit current through $G_L$?

How did you arrive at the second equation: $500i_2-4000(i_2-i_1)=0$ ?

The solutions are not correct.

figure 7 is missing

Part c) using Thévenin:

Thévenin's theorem is based on superposition and relies on simplifying the circuit connected to the load, to that of a voltage source with an internal resistance which (when connected to the load) forms a potential divider.

1) open circuit the load resistor between points a and b.

2) calculate the current flowing through R2 for the new circuit. $I = \frac{V_1}{R1 + R2}$

3) calculate pd across R2. $V_{R2} = \frac{V_1 R2}{R1 + R2}$

4) the p.d. across points ab is the same as V_R2 since these are in parallel.

5) replace the voltage source V₁ with a short circuit and calculate the equivalent circuit resistance between points ab with G_L omitted

6) redraw the circuit using the voltage calculated in 3) as the source with an internal resistance calculated in 5)

7) reconnect G_L to the new voltage source as described by 6) and calculate the current.

ANSWER = 3.43 mA (2 d.p.)

Using mesh currents, where the first loop has a clockwise current $i_1$ and the second loop has a clockwise current of $i_2$ and $G_L$ has a resistance value of $500\Omega$ because it has a value of 1mS which is the reciprocal of an Ohm, I think?

And on closer inspection, it should have a value of $1000\Omega$... Apologies, not sure if this is the cause of the problem?


They must be using a typesetter and the figure count has updated as they've taken a section out of the exam paper. Figure 7 is figure 5. Apologies.



With the new resistance value added, I get an $i_2$ value of 24mA. Why can I not use mesh currents to analyse this circuit, because the nodes a and b are shorted anyway, it isn't as if the circuit is open. Can you only use mesh currents if there is a source on the other loop?

1mS = 1000 ohms is correct.

You can use mesh but you have set up the loop equations incorrectly - specifically the second equation.

Nodes a and b are NOT shorted in Thévenin analysis.

Nodes a and b are opened.

The voltage source V1 is shorted.

Review Kirchoff's mesh method again more rigorously. They are simple errors but it's critical to get the methodology correct which means meticulous attention to detail i.e. current direction and hence +/- signs.

Perhaps you can help me with this question which is the same setup?
I get:
$i_3=i_1-i_2$
where $i_1$ and $i_2$ are the clockwise currents in the first and second loop respectively.
I end up with:
$-10+100i_1+100(i_1-i_2)=0$
and $100i_2+5+100(i_2-i_1)=0$
Simplifying to:
$300i_1=15$
leaving $i_1=0.05A$
$i_2=0A$
and $i_3=0.05A$.
Is this correct now?

Question as above.

My working:
Break each loop into its own current:
$-12+2000i_1+4000(i_1-i_2)=0$
$500i_2-4000(i_2-i_1)=0$
Simultaneous equations, solve:
$-2500i_2=-24$
Solutions:
$9.6 \times 10^{-3}=i_2$ and $8.4 \times 10^{-3}=i_1$

Is this right? If it is, how do I do part (d)? Thevenin's theorem is for working out the simplified circuit of Figure 5, why would I use it to work out the short-circuit current through $G_L$?

What course / year are you studying?

You seem to be having difficulty delineating the different methods for solving the problems.

They all take their roots from Kirchoff's rules, but the methodology for arriving at the answers are different.

Mesh analysis does not use the same methodology as Thévenins theorem, which itself does not use the same methodology as Superposition theorem and none are the same as Norton's theorem etc.

The questions are asking you to solve each problem using the stated method.


http://www.allaboutcircuits.com/vol_1/chpt_10/3.html

http://www.allaboutcircuits.com/vol_1/chpt_10/8.html

http://www.allaboutcircuits.com/vol_1/chpt_10/7.html

i'm also studying this, do you know of any books or anything which have lots of questions on this topic thanks

I'm studying BEng Electronic Engineering (Year 1).

I seem to have mislead you here, I know the question asked to use superposition theorem, but I wanted to try it using mesh currents because you noticed that I was having a problem with that particular analysis method. Apologies.