Find the Output Voltage Vo
Solve the given circuit using Kirchhoff's Current Law (KCL), Ohm's law, and the supernode method.
1. Given Circuit Parameters
Current source
1 mA
Resistors
1 kΩ
Each resistor
Voltage source
6 V
Required
Vo
2. Understand the Circuit
The circuit contains a 1 mA current source, four 1 kΩ resistors, and a 6 V source connected between the two midpoint nodes. The output voltage is measured between the top and bottom rails.
Reference node
Take the bottom rail as ground: 0 V. Let the top rail voltage be VT, and the left and right midpoint voltages be VL and VR.
Voltage source polarity
The longer battery plate is on the left. Therefore, VL − VR = 6 V.
Apply KCL at the Top Node
The 1 mA current source injects current into the top node. The current flows through the two upper resistors.
(VT − VL)/1kΩ
+
(VT − VR)/1kΩ = 1 mA
Multiplying through by 1 kΩ gives:
2VT − VL − VR = 1
Apply KCL Using the Supernode
Since the 6 V source connects the two midpoint nodes, treat both nodes as a single supernode.
Supernode KCL equation:
(VL − VT)/1kΩ
+
VL/1kΩ
+
(VR − VT)/1kΩ
+
VR/1kΩ = 0
Multiplying by 1 kΩ and simplifying:
2VL + 2VR − 2VT = 0
VT = VL + VR
Calculate the Top Rail Voltage
From Step 1:
2VT − VL − VR = 1
Using VT = VL + VR:
2VT − VT = 1
Therefore
VT = 1 V
Find the Midpoint Voltages
The voltage source gives the second equation:
VL − VR = 6
From Step 2:
VL + VR = 1
Adding the two equations:
2VL = 7
VL = 3.5 V
Substituting into VL + VR = 1:
VR = −2.5 V
Final Answer
The output voltage is measured from the top rail to the bottom rail. Since the bottom rail is ground:
Vo = VT − 0
Vo = 1.00 V
Rounded to two decimal places