Using combining independent sources and resistors, calculate the value of voltage v as shown in the below schematic:

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BlackTom AI · Accepted Answer

First, I restate the setup in my own words to ensure the circuit is interpreted correctly: the diagram shows a set of elements connected in parallel between a top node and a bottom reference node. In the leftmost branch there is a 13 A current source pointing upward (from bottom to top). Then there is a 5 Ω resistor in the next branch, a central branch with a 2 Ω resistor labeled with the voltage v across it (top positive), followed by a 4 A current source pointing downward, and finally a 3 Ω resistor on the far right. Since all elements are connected between the same two nodes, the voltage across every branch is the same and equals v (the top node potential minus the bottom node potential).

Now, apply KCL (sum of currents leaving the top node = 0). I will treat currents through the resistors as downward (from top to bottom) with magnitude v divided by their resistance. Thus:
- Current through the 5 Ω resistor: i5 = v/5 (leaving the top node downward).
- Current through the 2 Ω resistor: i2 = v/2 (leaving the top node downward).
- Current through the 3 Ω resistor: i3 = v/3 (leaving the top node downward).
- The 4 A source pushes current downward (leaving the top node): contributes +4 A to the leaving-top sum.
- The 13 A source pushes current upward (into the top node from below), which is opposite to leaving-top current, so it contributes -13 A to the leaving-top sum.

Set up the KCL equation:
v/5 + v/2 + v/3 + 4 - 13 = 0
Combine the resistive terms over common denominator 30:
(6v + 15v + 10v)/30 + (4 - 13) = 0
(31v)/30 - 9 = 0
Solve for v:
(31/30) v = 9  =>  v = 9 * 30 / 31 = 270/31 ≈ 8.71 V

Thus, the voltage v across the central branch is approximately 8.71 volts. Note: since the answer options were not provided in the prompt, the calculation above shows how to obtain v from the circuit using KCL and the parallel-resistor currents; you can verify by plugging v back into each branch current term and confirming the net current sums to zero.

Using combining independent sources and resistors, calculate the value of voltage v as shown in the below schematic:

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