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I need to solve exercise 57. I need to determine the voltage between points A and B in diagrams (a) and (b).

What I think so far:

  • The voltage on 10 ohm resistor is = 0.1A * 10Ω = 1V
  • The current on 20 ohm resistor will probably be 0.1A too (I think, I'm not sure). In this case its voltage is 2V (0.1A * 20Ω)
  • UAB = Upower-Ur1-Ur2 = 4.5V-2V-1V = 1.5 V

Is it correct?

Thanks for your help.

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    \$\begingroup\$ Remember that the current through two elements that are in series will always be the same. \$\endgroup\$ – Hearth Nov 6 '18 at 14:14
  • \$\begingroup\$ Then the two current will be 0.1A, so the voltage on 20 ohm resistor will be 2V? \$\endgroup\$ – T.Balazs Nov 6 '18 at 14:17
  • \$\begingroup\$ Indeed it will. \$\endgroup\$ – Hearth Nov 6 '18 at 14:18
  • \$\begingroup\$ And the AB voltage is correct what i have written? What will change on the results if the current flows in the another direction (b circuit version) ? \$\endgroup\$ – T.Balazs Nov 6 '18 at 14:20
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If we apply the first law of Kirchhoff we can tell that the current in both resistors (in both circuits) is the same, as you said. Thus, the voltage fall on the 10 ohm resistors is 1V and the other is 2V. Now, you have to apply the second law to determine V between A and B.

We need to add al voltages (including the source) and equal them to 0. The only thing to have in mind is the "direction" of that fall. In the first, is is against the direction so you'll need to substract, whereas in the second you'll need to add.

Vab1 = +1.5 V

Vab2 = -7.5 V

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  • \$\begingroup\$ Then on A circuit version : -The voltage's direction is always the same as current direction on passive components. -Then the kirchoff law : -1V+4,5V-2V=1.5V Circuit B version : -There the 10 ohm resistors current is in the opposite direction , so the voltage is in the opposite direction to. -Kirchoff law : 1V+4.5V-2V=3.5V Is 3.5 Volt correct ? I tryed but I cannot calculate out the -7,5V \$\endgroup\$ – T.Balazs Nov 6 '18 at 15:17
  • \$\begingroup\$ Why do you substract the 2V? they are all in the same "direction" so they all have the same sign. Either you add them all or you substract them all. The absolute value is 7.5 V and the sign depends on what you consider the "positive" direction to be. \$\endgroup\$ – José Antonio Font Nov 7 '18 at 8:18

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