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Unknown mesh currents will be always defined in the clockwise direction; known mesh currents i. In a circuit with n meshes and m current sources, n—m independent equations will result. The unknown mesh currents are the n—m independent variables. Apply KVL to each mesh containing an unknown mesh current, expressing each voltage in terms of one or more mesh currents. Solve the linear system of n—m unknowns.
Problem 3. Analysis: Label the nodes: v1, v2, and v3 as shown. Analysis: Label the nodes, v1, v2, and v3 as shown. Find: The branch currents through: a R1, b R2, c R3. Find: The voltage across each of the five resistors. Analysis: Assume a polarity for the voltages across R1 and R2 e.
R1 is connected between node A and ground; therefore, the voltage across R1 is equal to this node voltage. R2 is connected between node B and ground; therefore, the voltage across R2 is equal to this voltage.
The two node voltages are with respect to the ground which is given. Assume a polarity for the voltage across R3 e. Assume polarities for the voltages across R4 and R5 e. Find: The voltage Va. Assume that both mesh currents are clockwise. Known quantities: Circuit shown in Figure P3. Find: The voltages V1, V2, V3.
Solution: Known quantities: The current source value, the voltage source value and the resistance values for the circuit shown in Figure P3. Find: The three node voltages indicated in Figure P3. Find: The voltages Va, Vb Find: Power delivered to the load resistance.
Analysis: Add node V3 between the voltage source and its resistance, RV. Also, add the current i that flows through the voltage source. Choose the negative terminal of V0 as the ground reference node. KCL at node 1: Find: a Voltages b Write down the equations in matrix form. Solution: Circuit shown in Figure P3.
Find: Current 1i and 2i. Analysis: Meshes 1, 2 and 3 are clockwise from the left and are oriented clockwise. Find: Voltage across the current source. Analysis: The analysis for the mesh currents is exactly the same as Problem 3.
Solving, A Find: Mesh equation in matrix form. Collect coefficients and solve for the mesh currents. Find: Foura mesh equations and solve for currents. Write the node equations required to determine the node voltages. Write the matrix solution for each node voltage in terms of the known parameters. Solution: Known quantities: Circuit of Figure P3.
Find: a. The node equations required to determine the node voltages. The matrix solution for each node voltage in terms of the known parameters.
Analysis: a Specify the nodes e. Choose one node as the reference or ground node. If possible, ground one of the sources in the circuit. Note that this is possible here. When using KCL, assume all unknown current flow out of the node. The direction of the current supplied by the current source is specified and must flow into node A. The denominators are the same for both solutions. The main diagonal of a matrix is the one that goes to the right and down.
This is true only because there are no controlled dependent sources in this circuit. The most efficient way to solve for the voltage across R3.
Prove your case. The voltage across R3. Analysis: a There are 3 meshes and 3 mesh currents requiring the solution of 3 simultaneous equations. Only one of these mesh currents is required to determine, using Ohm's Law, the voltage across R3. If the terminal or node between the two voltage sources is made the ground or reference node, then three node voltages are known the ground or reference voltage and the two source voltages. A difficult choice.
Choose node analysis due to the smaller number of unknowns. Specify the nodes. Choose one node as the ground node. In KCL, assume unknown currents flow out.
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