How to Solve Electric Circuit Questions

[daewoo]

hey,
i'm having some trouble finding out the TOTAL resistance of the circuit shown below, what i have done is:
knowing its a combination series Rtotal = Rseries + Rparallel
R4 + R3 + (1/R1 + 1/R2)^-1 and i got an awnser of 37.5 Ohms, but i don't know if i did this correct, some of my friends got 25.0 Ohms, was hoping you could help me out,
Also another questin says what is the Current through R1 and R2, and i don't know how to do that, so if anyone knows please let me know,
thanks.

 

[lightgrav]

well, usually you know the battery Voltage.
Once you get the Effective R_eff of the whole circuit,
you can find the Current thru each series piece.
V across R_3||4 is this current I_batt times R_3||4 .
The Voltage V_3||4 = V_3 = V_4 , = I3 R3 = I4 R4 .

 

[Ouabache]

your friends are right, it is 25 ohms. R1 and R2 are not in parellel, they have R3 between them. Also R3 and R4 are not in series, as R1 is between them.

A typical approach. R2 and R3 are in series, combine them. Their combined R is in parallel with R1. Find the new combined R. The new R is now in series with R4. in other words: [(R2+R3) // R1] + R4 .

With that piece of information, you will know how to calculate the total current. Itot = V/Rtot (Actually i see they gave you total current on your diagram so you could have double checked your total resistance using R = V/I)

For second question, you can set up a couple of mesh (loop) equations and calculate I1 and I2. Such as
75-[R1*(I1-I2)]-[R4*I1] = 0 then [R2*I2]-[R3*I2] - [R1*(I2-I1)] = 0 . you have two equations, 2 unknowns (I1, I2) just solve for them.

Or you could set up a nodal equation. You know 3A is going to split some way thru R1 and R2. The top node Va = 75v. There is also a bottom node, let's call it Vb between R3 and R4. A nodal equation may be written (Va-Vb)/R1 + (Va-Vb)/(R2+R3) + Itot = 0 You know Va, solve for Vb. I1 = (Va-Vb)/R1 and I2=(Va-Vb)/(R2+R3).

 

[verty]

These questions look difficult but they aren't. Follow my logic here.

You have the battery voltage and total current, so total resistance R = V/I = 25 Ohms. That's it, part one done.

For the second part, let's be smart. Have a look at R4. You know the current going through R4 is 3A, so you can calculate the volt-drop over R4: V4 = I*R4. The trick now is to see that the voltage over R1 is the total voltage minus V4. Do you see that?

Now you can calculate the current through R1. The second trick is that the 3A total current is split between the R1 and the R2+R3 branch, so you can calculate the current through R2. That's part two done.

Go over what I have said carefully, make sure you understand each step and why it works. These tricks I used, know them and when to use them, otherwise you will suffer with these circuit questions.

 

[Ouabache]

The methods I shared (mesh current-loops and nodal equations) are the standard approach taught for working with all linear circuits. If you are only just learning about these circuits, I would hold off trying clever approaches.

Vertigo does suggest valid shortcuts. If this question were given on an exam and you had a limited time to work on them; then if you were to notice those relationships and you felt confident using them, it would be a quicker way to go. If you have any doubts using the clever appoach correctly and if you are not time-limited, try the approaches I gave. They both need to agree. If two methods agree, it increases your confidence that you have the right answer.