The algebraic sum of all currents entering a node must always be zero where inis the nthcurrent. N is the number of branches.A common assignment: 1.if the current is entering the node, assign a negative “-“sign and 2.if the current is leaving the node, assign a positive “+” sign.For the following figureThe node equation can be written as To use KCL to analyze a circuit,1.Write KCL equations for the currents2.Use Ohm’s law to write currents in terms of bode voltages (one equation for each resistor)3.Solve to find values of node voltage and current
Example: Find the current through a 20Ω resistance, and current through a 40Ω resistance
Write KCL at node x Write in the circuit using Ohm’s Law Apply last two equation into KCL at node x The current through a 20Ω resistance The current through a 40Ω resistance
where v n is the n th voltage. N is the number of elements in the loop A common assignment: 1. if the positive (+) side of the voltage is encountered first, assign a positive “+”sign to the voltage across the element. 2. If the negative (-) side of the voltage is encountered first, assign a negative “-”sign to the voltage across the element. For the following figure To use KVL to analyze a circuit, 1. Write KVL equations for voltages 2. Use Ohm’s law to write voltages in terms of resistances and currents. 3. Solve to find values of the currents and then voltages.
Examples: Example 2 : Find the current i and voltage v over the each resistor.
KVL equations for voltages Using Ohm’s Law Substituting into KVL equation
Example 3: Find v1 and v2 in the following circuit(note: the arrows are signifying the positive position of the box and the negative is at the end of the box) Loop 1Loop 2Example 4: Find V1, V2, and V3.(note: the arrows are signifying the positive position of the box and the negative is at the end of the box)
Loop 1 Loop 2 Loop3 Example 5: Find V1, V2, V3,and V4 (note: the arrows are signifying the positive position of the box and the negative is at the end of the box)
Loop 1 Loop 2 Loop 3 Loop 4
Practice Problems: (Click image to view solution) Problem 1: Find V1 in the following circuit.Problem 2: Find V0 in the following circuit.Problem 3:Find V1,V2, and V3 in the following circuit.
Problem 4 : Find I 1 ,I 2 , I 3 in the following circuit Problem 5 : Find the resistor R value in the following circuit. Exercises:
1.V1=8V, V2=-4V, V4=14V. Find V3and V5in the following circuit2.Find Vxand Vyin the following circuit3.Find Vx, Vyand Vzin the following circuit
4.Find the KCL node equations at nodes A,B,C, and D5.If I1=4A , I2=5A, and I3=3A, then using KCL find I4and, I5in the following circuit Answers: 1. V 3 =12V and V 5 =-2V 2. V x =12V and V y =9V 3. V x =35V, V y =5V, and V z =15V 4. At node A: At node B: At node C: At node D: 5. I 4 =2A and I 5 =1A Survey:
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- Fall '19
- Kirchhoff's circuit laws, Voltage drop, Kirchhoff