kvl kcl- nodal analysis
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This document discusses nodal analysis, a technique for analyzing electrical circuits where the voltages at different nodes of the circuit are calculated. It provides examples of applying Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) to set up equations relating the currents and voltages in a circuit containing resistors connected in a mesh. The document explains how to use these equations to solve for the unknown voltages at each node of the circuit.
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Basic of circuit
Charge
Charge is an electrical property of the atomic particles which matter consists.
The unit of charge is the coulomb (C).
The symbol for the charge is Q (or) q.
ퟏ풄풐풖풍풐풎풃=ퟏ/(ퟏ.ퟔퟎퟐ×〖ퟏퟎ〗^(−ퟏퟗ) )=ퟔ.ퟐퟒ× 〖ퟏퟎ〗^ퟏퟖ 풆풍풆풄풕풓풐풏풔
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The symbol for the current is I (or) i.
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The potential difference between two points in an electric circuit called voltage.
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Voltage is represented by V (or) v.
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Power is the rate at which energy is expanded or the absorbing.
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Example:
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The inductance of element is denoted by the symbol “L”.
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The capacitance of element is denoted by the symbol “C”
It is measured in Farads (Ϝ).
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kvl kcl- nodal analysis
- 3. R1 R2 R3 c a b c a b Rc Ra Rb Delta or ∆ Wye or Y R R R R R R R R R R R R R R R R R R a b c = + + = + + = + + 1 2 1 2 3 2 3 1 2 3 1 3 1 2 3 Wye-Delta Transformation R R R R R R R R R R R R R R R R R R R R R R R R a b b c a c b a b b c a c c a b b c a c a 1 2 3 = + + = + + = + + Y to Δ Equations Δ to Y
- 4. Kirchhoff’s Voltage Law, KVL 3 V R1 2.2 k R2 3.7 k R4 5.4 k R3 1.0 k 1 2 3 0 + VR1 - - VR2 + - VR4 + - VR3 + Loop (0, 1, 2, 0) V0,1 + V1,2 + V2,0 = 0 V -3 V + VR1 - VR3 = 0 V Loop (0, 3, 2, 0) V0,3 + V3,2 + V2,0 = 0 V VR4 + VR2 - VR3 = 0 V For example: V1,2 = - V2,1 = VR1
- 5. Nodal Analysis 1 entering leaving A current is entering the node if the current is leaving the device. A current is leaving the node if the current is entering the device.
- 6. Nodal Analysis 2 Apply Ohm’s Law (I = V/R) for R1: current entering node 2 = (V1 - V2) / R1 current leaving node 2 = (V2 - V1) / R1 R1 1.5 k1 2
- 7. Kirchhoff’s Current Law, KCL KCL at node 2: Σ ΣI I I I I V V V V V V entering leaving R R R = + = − + − = − 1 3 2 1 2 0 2 2 3 2 2 1 3. k .0 k .7 k Shade indicates a node At node 1, V1=3 v. due to source At node 0, V0=0 v. due to ground KCL at node 3: V V V V2 3 3 0 3 7 − = − . k 5.4 k 3 V R1 2.2 k R2 3.7 k R4 5.4 k R3 1.0 k 1 2 3 0 IR1 IR2 IR3 IR2 IR4
- 8. Nodal Analysis Shade indicates a node 3 V R1 2.2 k R2 3.7 k R4 5.4 k R3 1.0 k 1 2 3 0 IR1 IR2 IR3 IR2 IR4 Substitute the known voltages into the equations that were obtained at nodes 2 & 3 Solve the two equations for V2 and V3 You can put the two equations in matrix form and solve using Matlab or any mathematics program (or your calculator).