Question

Determine the voltage of U_ab using Kirchhoff's laws

Answer 1

`V_(ab)=4\text{ V}`

Step-by-step explanation:

You want the voltage between nodes 'a' and 'b' given the branch resistances and currents shown.

Ohm's law

To find the voltage between nodes 'a' and 'b', one only need apply Ohm's law:

V = IR

Vab = (2 A)(2 Ω) = 4 V

The voltage between nodes 'a' and 'b' is 4 volts.

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Additional comment

The two voltage sources are ...

• E1 = 3 V
• E2 = 13 V

These can be found by applying Kirchoff's Current Law: the sum of currents into a node is zero, and Kirchoff's Voltage Law: the sum of voltages around a loop is zero.

These mean the 1A current will add to the 2A current to produce 3A in the 3Ω resistor. The voltage Vab is the same for all parallel branches, so the 1V drop in the 1Ω resistor needs to be added to the 3V of E1 to make 4V. The 9V across the 3Ω resistor is subtracted from the 13V of E2 to make 4V. (The source E2 is driving current into the "source" E1.)