This is one of question in my project: In the circuit diagram, which way does the current flow? Can you calculate the current through the each resistor and the resistance of R4?

Can i use the Millman's therom to determine which way does the current flow?

V1= V through R1 AND R2
V2= V through R4
V3= V through R3 AND R5

(I1 + 0 +I3)/((1/(R1+R2))+ 0 + (1/(R3+R5)))
=6V

So the answer of 6 volts is the voltage seen across all parallel branches, and because the p.d between two supplies are 4V, current will flow through R4 from the junction between R2 and R3.

The current flow through R4 would be:
(8/25-4/25)=0.16A ( short circuit)

Is my answer correct? Plz tell me if there is any error , thx

 

Your answer is not correct as written. Mainly because you have 0 in the denominator for the admittance of R4.

You can use Millman's to write the expression for the voltage across R4 in terms of all of the other circuit values given, but you are going to need some additional information if you are to get to the final value of resistance for R4 and the current flowing in it.

Is it possible that there is some additional information that goes with this problem that has been omitted from your post?

In case you have not already happened across the material in the "All About Circuits" ebook, here are a couple of links.

All About Circuits Tutorial on Millman's Theorem

Additional Info on Millman's Theorem here at AAC


hgmjr

 

When you simplify the theorem, you will get:

V = (.16) / (.08 + (1 / R4))

There are 2 unknowns, V, and R4.

 

As antseezee has shown, Millman's Theorem analysis can be used to produce a single equation containing two unknowns.

The V in antseezee's equation is the voltage across R4 referenced to the circuit node where R4 and the two voltage sources converge.

What is needed is an additional bit of information to completely determine the value of R4 along with the current that is flowing in R4.

Here is a Millman's Theorem Equation for your circuit.

hgmjr

 

Thx for helping. I also got another question which is similar to this but i had been given the resistance of all the resistors, i solved that with the thevein theorem:
Ignore the resistor in b2
Total voltage: 10+5V/10-5V
Total resistance:11 Ω

Should the total voltage in the series be (10+5)V or (10-5)V? In theory, i reckon should be (10-5)V.According to the tutorial http://www.allaboutcircuits.com/vol_1/chpt_10/8.html , the positive terminals of both power supplies are facing up, so the total voltage should be 21V. If one of the positive terminal face up and the other one face down like the attached picture, do we still have 21 V as the total voltage:confuse:

 

Using Thevenin's Theorem, you should be able to temporarily ignore the existence of R1 and the 10V dc source while you focus your attention on calculating the Thevenin voltage and the Thevenin impedance associated with the 5V dc source, R2, R3, and R5.

You should end up with the value for Vth and Rth that is acting on the circuit node at the convergence of R1, R2, and R3.

Give that calculation a try and then post your efforts here.

hgmjr