Anonymous
Anonymous asked in Science & MathematicsPhysics · 2 months ago

What is the potential difference between points a and b? ?

My Analysis : We can divide this into 2 circuits.

1) 16V - 2 Resistors in series, total R = 16 Ohm , Total Current = 1A

2) 18V - 2 Resistors in series, total R = 20 Ohm, total Current = 0.9A

Voltage drop at (a) from 1) = -4V , from 2) -10.8 , totally -14.8 at a

at b) from 1) we have +18V because it gains voltage as it is going towards the negative end of the battery ( I have a doubt here )

from 2) it is 0 ..

So the difference is 18 - 14.8 = 3.2V , but this is incorrect it says the answer is 12V

Please help. Thank you.

Attachment image

2 Answers

Relevance
  • 2 months ago
    Favorite Answer

    Here is a method that is very easy for these types of circuits. This ckt has three branches, each of which has a unique current. By KCL( the current in = the current out). The sum of the 3 currents = 0. Let "b" = ground and "a" = node V. Sum the currents LEAVING  node V (right to left) to = 0:

    (V-16)/4Ω + (V-18)/12Ω + V/8Ω = 0

    Multiply the equation by 24 (common denominator)

    6(V-16) + 2(V-18) + 3V = 0

    Expand equation:

    6V- 6*16 + 2V - 2*18 + 3V=0

    Collect terms:

    11V - 96 - 36 = 0

    11V = 96+36 = 132

    V = 132/11 = 12v but V = Vab

    Vab = 132/11 = 12v <<<<<<<

    The current in the top branch

    (12v-16v)/4Ω = -1 or +1A left to right.

    The current in the middle branch

    (12v-18v)/12Ω = -0.5 or +0.5A left to right

    The current in the bottom branch

    12/8 = 1.5A right to left.

    If you plug these current into the circuit, KVL and KCL are satisfied.We could also check by verifying the power delivered by the sources = the power consumed by the resistances:

    From Sources P = V*i

    16v*1A +18v*0.5A = 25W

    Consumed by resistance P = i²*R:

    1²*4Ω+(1/2)²*12+(1.5)²*8 = 25W Checks.

    I hope this helps. Please award Best Answer to the best answer as this is the only reward for efforts to help.

    • ...Show all comments
    • oldschool
      Lv 7
      2 months agoReport

      Writing proper equations reduces circuit analysis to solution of multiple equations which is algebra.

    • Login to reply the answers
  • Anonymous
    2 months ago

    Do your own homework.  No one around here ever bothers giving best answer anyway.

    • Login to reply the answers
Still have questions? Get your answers by asking now.