Please help me in this question on network ?

[munna007]

Hello friends...in this questions the answer is (b) option...this is from indian engg. services exam.

if we apply mesh in loop which i have shown , then we find that

I = (10 - 5 )/10 = 0.5 amp


V=10 - 6 I = 7 volt (right acc. to answer keys)

and Rth = 2.4 ohm (i have calculated Rth)


but if we apply Nodal analysis where V is marked then

acc to that
(V-10)/6=(V-5)/4
V= -5

so we see that both results are not equal...but in answer keys 7 volt is given...
please tell me what is the problem in second method of nodal analysis.? is this wrong ?



thanks in advance...

 

[vk6kro]

V= 10 - (volts across 6 ohms) because these have opposite polarities.

so (volts across 6 ohms) = 10 - V

Current in 6 ohms = (10 - V) / 6

Then it works out.

40 - 4 V = 6V - 30

10 V = 70

V = 7

 

[munna007]

thanks for reply sir...can u please tel me how u have said

V=10 - (voltage across 6 ohm)

please explain with detail...

and is not V and 10 volt same thing ? n so i think it should be V=10+V6

 

[gneill]

but if we apply Nodal analysis where V is marked then

acc to that
(V-10)/6=(V-5)/4
V= -5

You are applying nodal analysis, calculating the current in each branch from the node where V is located. The sum of these currents (leaving the node) must total zero. What you've written equates the currents in each branch -- this is not quite right -- these currents will be equal and opposite if the sum of currents is to be zero.

So write instead,

(V-10)/6 + (V - 5)/4 = 0

and see how things go...

 

[vk6kro]

In this diagram,

[PLAIN]http://dl.dropbox.com/u/4222062/loop.PNG

If you look at the polarity of the left branch, then V = 10 - ( voltage across the 6 ohm resistor).

Since the currents in each resistor must be the same it is valid to work out these currents in terms of V and then solve for V.

In the right branch, current is flowing downwards so the polarities add up the screen and these must also equal V.

 

[munna007]

thanks a lot sir...i understood mistake done by me...