# Hard Circuit simplification problem

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1. Aug 11, 2016

### rohanlol7

1. The problem statement, all variables and given/known data
Everything is in the picture. Question 3(a)
This is for preparation for a contest.

http://i.imgur.com/FtiKaYw.jpg

2. Relevant equations
V=IR

3. The attempt at a solution
I calculated the total resistance of the first circuit and used that to evaluate V(AB). But this is in terms of the resistance of the load. I tried using kirchoffs laws to eliminate it but i cannot seem to do so. Also i do not understand why there is a unique combination of R(th) and E(th) that works.
I also noticed that R(th) is in face the value of the resistance of the first circuit if the load has zero resistance but i dont understand why this is so

Last edited by a moderator: Aug 15, 2016
2. Aug 11, 2016

### BvU

Look at it from the point of view of the load. And post your work to see where you get stuck...

3. Aug 11, 2016

### cnh1995

Look up Thevenin's theorem. Eth is the Thevenin equivalent voltage and and rth is the Thevenin resistance.

4. Aug 11, 2016

### rohanlol7

Thanks ! i saw it. However i still don't understand how i'm supposed to figure that out in the problem

5. Aug 11, 2016

### BvU

You have two equations (already filling in $\ \ V_{AB} = V_{PG} = V_L \ \$ and $\ \ I=I_0={V_L\over R_L}\$) : $$V_L = V_{th}\; {r_{th} \over r_{th} + R_L}$$ in the right diagram; and in the left diagram you have $$V_1 \; {R_3 \over R_1 + R_3} = V_L + R_2 {V_L \over R_L}$$and your task was to work around these two equations with four unknowns to two relationships by eliminating $V_L$ and $R_L$. Not so easy, I grant you. But thereby you prove Thevenin's theorem (as opposed to making use of it)

6. Aug 11, 2016

### rohanlol7

Thanks ! i tried something similar.
The second equation come from equating the pd accross R3 right ?

7. Aug 11, 2016

### BvU

Across R3 and across the series Rload and R2 as well

8. Aug 11, 2016

### rohanlol7

The right hand side of the equation represents the pd across the load and R2( right ? ) shouldnt the left hand side be v1- v1*R1/(total resistance for the circuit) ?

9. Aug 11, 2016

### BvU

My bad ! Sorry. Well observed !

10. Aug 11, 2016

### rohanlol7

No problem!
God so i knew how to do it its just the maths part thats killing me. I guess i'll have to work that out slowly. Thanks!