In a circuit with a current source of 3 A in parallel with a 6 Ω resistor connected to a node, determine node voltage if the node also connects to a 12 Ω to ground.

In a circuit with a current source of 3 A in parallel with a 6 Ω resistor connected to a node, determine node voltage if the node also connects to a 12 Ω to ground.

• A. 6 V
• B. 9 V
• C. 15 V
• D. 12 V

Answer: (D)

When a node has a current source injecting current into it and resistors to ground, the node voltage rises until the currents through those resistors sum to equal the injected current. This is the essence of applying Kirchhoff’s current law at the node. Here, the current source pushes 3 A into the node. The two resistors to ground draw currents equal to V/6 and V/12, respectively. So the current balance is V/6 + V/12 = 3. Combine the terms: V(1/6 + 1/12) = V(2/12 + 1/12) = V/4. Set this equal to 3 A and solve: V/4 = 3 → V = 12 V. Therefore, the node voltage is 12 volts.

When a node has a current source injecting current into it and resistors to ground, the node voltage rises until the currents through those resistors sum to equal the injected current. This is the essence of applying Kirchhoff’s current law at the node.

Here, the current source pushes 3 A into the node. The two resistors to ground draw currents equal to V/6 and V/12, respectively. So the current balance is V/6 + V/12 = 3. Combine the terms: V(1/6 + 1/12) = V(2/12 + 1/12) = V/4. Set this equal to 3 A and solve: V/4 = 3 → V = 12 V. Therefore, the node voltage is 12 volts.