Solve Node Voltage Equations for Circuit w/ 10V Power Source

In summary, the node above the 10 V power source is +20 V above ground. The node just above the 10 V source is -10V with respect to ground, i.e. the negative terminal of the 20 V source. The unknown voltage V1 is a nice round number and can be found by using that answer to figure out the 3 unknown currents flowing in/out of the V1 node.
  • #1
lostinhere
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Can anyone help me find node-voltage equations for this circuit. The 10V power source is throwing me. Thanks.
 

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  • #2
Taking the - terminal of the 20V source as reference, or ground, the node above the 20 V source is +20 V above ground.


The node just above the 10 V source is -10V with respect to ground, i.e. the negative terminal of the 20V source.
 
  • #3
I have this much
Node 1: between the 25k resistor and the 11mA source)
node 2: between the 500 ohm resitor, 10v source, 1k resistor and 500 resistor and the 11mA source
V1: voltage across the 250 resistor
V2: voltage arcross the 1k resistor
reference node at the bottom of the pic
node1: (V1-20)/25K+V1/250+.011+(V1-V2)/500=0
node2: -.011+V2/1000+(V1-V2)/500+...=0

I'm not quite sure how to hande the 10v supply.
 
Last edited:
  • #4
.....nvm
 
  • #5
lostinhere said:
I have this much
Node 1: between the 25k resistor and the 11mA source)
node 2: between the 500 ohm resitor, 10v source, 1k resistor and 500 resistor and the 11mA source
V1: voltage across the 250 resistor
V2: voltage arcross the 1k resistor
reference node at the bottom of the pic
node1: (V1-20)/25K+V1/250+.011+(V1-V2)/500=0
node2: -.011+V2/1000+(V1-V2)/500+...=0

I'm not quite sure how to hande the 10v supply.
There's only one unknown -- the voltage V1. Call the bottom rail ground, then you only have to solve for V1 to know all the voltages and currents in the circuit. The V2 is just -10V, set by the voltage source on the right.

The answer for V1 is a nice round number (hint), and you can check your work by using that answer to figure out the 3 unknown currents flowing in/out of the V1 node. They should sum to zero, or you didn't solve your node 1 equation above correctly.

Post the answer!
 
  • #6
its so easy and so basic...my professor gives us too complicated circuits..
 

1. How do I solve node voltage equations for a circuit with a 10V power source?

To solve node voltage equations for a circuit with a 10V power source, you will need to use Kirchhoff's Current Law (KCL) and Ohm's Law. First, label each node in the circuit and assign a variable for the unknown voltage at each node. Then, use KCL to write an equation for each node, setting the sum of the currents entering and leaving the node equal to 0. Next, use Ohm's Law to convert the current equations into voltage equations. Finally, solve the system of equations to find the voltage at each node.

2. What is Kirchhoff's Current Law?

Kirchhoff's Current Law (KCL) states that the sum of the currents entering and leaving a node in an electrical circuit must equal 0. This means that the current flowing into a node must be equal to the current flowing out of the node, or in other words, charge is conserved at a node in a circuit.

3. How do I use Ohm's Law to solve node voltage equations?

To use Ohm's Law in node voltage equations, you will need to convert the current equations into voltage equations. Ohm's Law states that the voltage (V) is equal to the current (I) multiplied by the resistance (R). So, for each current equation, substitute in Ohm's Law to solve for the voltage at each node.

4. How many equations do I need to solve for node voltages in a circuit with a 10V power source?

In a circuit with a 10V power source, you will need to write an equation for every node in the circuit. This means that the number of equations needed will depend on the number of nodes in the circuit. For example, if there are 3 nodes, you will need to write 3 equations and solve for 3 unknown voltages.

5. Can I use node voltage equations to solve for any circuit?

Yes, node voltage equations can be used to solve for any circuit, as long as the circuit is linear and contains only voltage sources, resistors, and current sources. Non-linear components, such as diodes or transistors, would require a different approach to solving the circuit.

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