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# 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.

### 2 Answers

- oldschoolLv 72 months agoFavorite 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.

- Anonymous2 months ago
Do your own homework. No one around here ever bothers giving best answer anyway.

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