Question: What is the current flowing in each branch of the circuit shown below? Do voltage sources act as generators or sinks? What are the values of the internal resistances of the sources? The batteries and the power supply are real voltage sources (they are a source of electromotance εi and include an internal resistance ri). The potential differences across the voltage sources are given by ∆Vi. You need to get the mathematical expressions to evaluate the following quantities: the current that flows through each branch in a closed circuit, the voltage across each source in open and closed circuits, and the internal resistance of each source. Method: 1. Draw the circuit diagram, with all potential differences and resistances. For this circuit, the potential differences across the voltage sources (∆Vi) and the resistances (Ri) are measured quantities and the currents (Ii) in the branches are the unknowns. We do not know the internal resistance (ri) of the voltage sources, so we cannot use εi and ri here. 2. Assume a different current for each circuit branch and indicate it on the diagram, with its hypothetical direction. Use Ii for the left branch, I2 for the middle branch, and I3 for the right branch.
DC circuit
Question: What is the current flowing in each branch of the circuit shown below? Do voltage sources act as generators or sinks? What are the values of the internal resistances of the sources?
The batteries and the power supply are real voltage sources (they are a source of electromotance εi and include an internal resistance ri). The potential differences across the voltage sources are given by ∆Vi.
You need to get the mathematical expressions to evaluate the following quantities: the current that flows through each branch in a closed circuit, the voltage across each source in open and closed circuits, and the internal resistance of each source.
Method:
1. Draw the circuit diagram, with all potential differences and resistances. For this circuit, the potential differences across the voltage sources (∆Vi) and the resistances (Ri) are measured quantities and the currents (Ii) in the branches are the unknowns. We do not know the internal resistance (ri) of the voltage sources, so we cannot use εi and ri here.
2. Assume a different current for each circuit branch and indicate it on the diagram, with its hypothetical direction. Use Ii for the left branch, I2 for the middle branch, and I3 for the right branch.
Identify the number of meshes (closed courses) and label it on the diagram.
3. Apply Kirchhoff's law of knots.
Use Kirchhoff's mesh law to obtain the sum of potential differences across all elements of each useful mesh (use closed-circuit voltages ∆Vi for voltage sources). Make sure your signs are correct. Use Ohm's Law to find the potential difference across each resistor. Check that the number of linear equations you wrote above agrees with the number of unknowns.
4. You can now solve your equations and obtain mathematical expressions for the currents Ii in each branch as a function of the closed-circuit voltages ∆Vi and the resistances Ri.
5. Write an equation to find the internal resistance of the sources from the known measurements and the equations of the currents obtained in 4.
6. Do the sources act as generators or as receivers? Explain.
Step by step
Solved in 4 steps with 1 images
