Find the potential difference of A and B
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As per the question, we have to find out the potential difference between points A and B.
So, first find out the net resistance of the circuit
Therefore R eq. = 4+4+12 =20 ohms.
Therefore net current in the circuit
I = V/(R eq.)
=> I = (6-4)/20
=> I = 2/20 = 0.1 amperes
Now you have to apply Kirchoff current law. In simple words, start from a point , note the potential drops and end at another point.
Let potential at point A be VA,
and at point B be VB.
Now I will start from A and end at B and note the potential differences along the way.
VA + I*4 + 4 = VB
=> VA - VB = -4 - (0.1*4)
=> ∆V = - 4.4 volts
The answer is -4.4 volts.
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