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## Homework Statement

R1 = 2 ohms

R2 = 4 ohms

R3 = 6 ohms

E1 = 10 V

E2 = 14 V

What is the voltage between point A and B ?

A. 0.18 V

B. 0.98 V

C. 1.34 V

D. 1.64 V

E. 3.28 V

## Homework Equations

KVL

## The Attempt at a Solution

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I tried using KVL

I assume that both mesh currents will go in clock-wise direction.

x = current goes in lower mesh

y = current goes in upper mesh

So, the current that goes through AB or I

_{3}is (x-y)

For the lower mesh,

E

_{2}- I

_{3}R

_{3}- x R

_{1}

14 - 6(x-y)-2x = 0

For the upper mesh,

4y - 10 - 6 (y-x) - 14 = 0

Solve for x and y..

x = 5.8 A

y = 5.4 A

So, the current goes through AB is 0.4 A

So,

Vb = 14 - 6 (0.4) = 11.6 V

Va = 11.6 - 2(5.8) = 0 V

So, I think Vab = Va - Vb = -11.6 V

But, it's not in the option..

However, this is the book answer

I have no idea what methods are used to solve this very quickly.

Please help

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