Current and Electricity Question

[draotic]

i got it until ' R P(1) = 3 ohm '
but shouldn't the effective resistance of arm ADE be 6+3=9
and effect. resistance b/w A & E be (9*6) / 9+6 = 54/15 ?

 

[azizlwl]

Why is it you say ADE, 6+3 not 3+3?

Going from A->D->E, A->D, 2 parallel resistors. D->E only one resistor.

 

[draotic]

please help me to understand how to calculate resistances in arms like the above e.g. .

 

[Kavik]

You have to simplify one branch at a time where resistors are clearly either in series or parallel. Starting at the left branch, it begins to simplify like so:

[1] Recognize that the two 3Ω resistors are in series, add them: 3Ω + 3Ω = 6Ω. Replace that resistor in next step.

[2] With the new 6Ω resistor in place we now recognize that it is in parallel with the AD 6Ω resistor, so we do the math to simplify them: 6Ω || 6Ω = 3Ω

[3] The 3Ω resistor replaced the previous parallel ones.

With these simplifications we see that the "arm ADE" is actually the equivalent of two 3Ω resistors in series, thus 6Ω.

Also, I don't like how your book uses phrases like "Therefore Effective Resistance between A and E is given by." This is confusing, as it is only one path between points A and E, NOT the equivalent resistance. The true effective resistance between A and E would be when all resistors in the diagram are simplified down to one resistance (with respect to A and E, e.g. when all that remains is one resistor in between point A and point E).

Hope that helps.

 

[draotic]

You have to simplify one branch at a time where resistors are clearly either in series or parallel. Starting at the left branch, it begins to simplify like so:

[1] Recognize that the two 3Ω resistors are in series, add them: 3Ω + 3Ω = 6Ω. Replace that resistor in next step.

[2] With the new 6Ω resistor in place we now recognize that it is in parallel with the AD 6Ω resistor, so we do the math to simplify them: 6Ω || 6Ω = 3Ω

[3] The 3Ω resistor replaced the previous parallel ones.

With these simplifications we see that the "arm ADE" is actually the equivalent of two 3Ω resistors in series, thus 6Ω.

Also, I don't like how your book uses phrases like "Therefore Effective Resistance between A and E is given by." This is confusing, as it is only one path between points A and E, NOT the equivalent resistance. The true effective resistance between A and E would be when all resistors in the diagram are simplified down to one resistance (with respect to A and E, e.g. when all that remains is one resistor in between point A and point E).

Hope that helps.

ok , i think i got it
thank you very much sir...
appreciate what you are doing !