Do you see thatthere are three loops to choose from? Did you choose two of them?

Question

Do you see thatthere are three loops to choose from? Did you choose two of them?Did you draw a current for two of the branches? You need to giveeach a name and a direction. Did you somehow combine them (theyeither subtract or add) to symbolize the current in the thirdbranch? As you walked around two of the loops (full loop), did youwrite a loop equation of the potential differences you encountered?VERY IMPORTANT: Did you get the signs of those potentialdifferences correct? Once you have the currents, did you walk frompoint b to point a, keeping track of thepotential differences along the way?

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battery 1 1 A battery 2 2 A battery 3 3 A

Explanation / Answer

   we take that R1 resistors occurin series pairs contributing net resistances 2 R1 ineach branch where they appear    as 2 =3    R2 = 2 R1    the currents through 2 and3 are the same as    i2 = i3        = i    so the current through 1 isi1 = 2 i    Vb - Va =2 - i R2                 =1 + 2 R1 2 i    so the current will be    i = (2- 1) / (4 R1 +R2)      = ........ A    the current through    i1 = 2 i       = ........A      direction is downward (b)    the current through    i2 = i       = ........A      the directon is upward (c)    the current through    i3 = i2       = ........A      the directon is upward (d)    Va - Vb = - i R2+ 2                = ......... V       = ........A      the directon is upward (d)    Va - Vb = - i R2+ 2                = ......... V

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