Circuit theorem
- 1. TOPIC DC Circuit Theorem Presented By, Mohammad Monowar Hossain Munna, ID: 163-33-3756 Section: B Daffodil International University Dept. of Electrical and Electronics Engineering
- 2. Ohm's Law The potential difference (voltage) across an ideal conductor is proportional to the current through it. The constant of proportionality is called the "resistance", R. Ohm's Law is given by: V = I R where V is the potential difference between two points which include a resistance R.
- 3. Kirchhoff's Laws Kirchhoff's circuit laws are two equalities that deal with the conservation of charge and energy in electrical circuits. There basically two Kirchhoff's law :- 1. Kirchhoff's current law (KCL) – Based on principle of conservation of electric charge. 2. Kirchhoff's voltage law (KVL) - Based on principle of conservation of energy.
- 4. The current entering any junction is equal to the current leaving that junction. i1 + i4 =i2 + i3 Kirchhoff's current law (KCL)
- 5. Kirchhoff's voltage law (KVL) The sum of all the voltages around the loop is equal to zero. v1 + v2 + v3 - v4 = 0
- 6. Mesh Analysis Mesh analysis (or the mesh current method) is a method that is used to solve planar circuits for the currents (and indirectly the voltages) at any place in the circuit. Planar circuits are circuits that can be drawn on a plane surface with no wires crossing each other. Mesh analysis works by arbitrarily assigning mesh currents in the essential meshes. An essential mesh is a loop in the circuit that does not contain any other loop.
- 7. Example A circuit with two meshes.
- 8. Apply KVL to each mesh. For mesh 1, For mesh 2, 123131 213111 )( 0)( ViRiRR iiRiRV 223213 123222 )( 0)( ViRRiR iiRViR
- 9. Nodal Analysis In electric circuits analysis, nodal analysis, node- voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents. Nodal analysis is possible when all the circuit elements branch constitutive relations have an admittance representation. Kirchhoff’s current law is used to develop the method referred to as nodal analysis
- 10. 1. Reference Node The reference node is called the ground node where V = 0 + – V 500W 500W 1kW 500W 500W I1 I2
- 11. Example V1, V2, and V3 are unknowns for which we solve using KCL 500W 500W 1kW 500W 500W I1 I2 1 2 3 V 1 V 2 V 3
- 12. Currents and Node Voltages 500W V1 500WV1 V2 W 500 21 VV W500 1V
- 13. 3. KCL at Node 1 500W 500W I1 V1 V2 W W 500500 121 1 VVV I
- 14. 3. KCL at Node 2 500W 1kW 500W V2 V3V1 0 500k1500 32212 W W W VVVVV
- 15. 3. KCL at Node 3 2 323 500500 I VVV W W 500W 500W I2 V2 V3
- 16. Superposition Theorem The total power delivered to a resistive element must be determined using the total current through or the total voltage across the element and cannot be determined by a simple sum of the power levels established by each source For applying Superposition theorem:- Replace all other independent voltage sources with a short circuit (thereby eliminating difference of potential. i.e. V=0, internal impedance of ideal voltage source is ZERO (short circuit)). Replace all other independent current sources with an open circuit (thereby eliminating current. i.e. I=0, internal impedance of ideal current source is infinite (open circuit).
- 17. Example:- Determine the branches current using Superposition theorem. Solution: The application of the superposition theorem is shown in Figure 1, where it is used to calculate the branch current. We begin by calculating the branch current caused by the voltage source of 120 V. By substituting the ideal current with open circuit, we deactivate the current source, as shown in Figure 2. 120 V 3 W 6 W 12 A4 W 2 W i1 i2 i3 i4 Figure 1
- 18. To calculate the branch current, the node voltage across the 3Ω resistor must be known. Therefore 120 V 3 W 6 W 4 W 2 W i' 1 i' 2 i' 3 i' 4 v1 Figure 2 42 v 3 v 6 120v 111 = 0 where v1 = 30 V The equations for the current in each branch,
- 19. In order to calculate the current cause by the current source, we deactivate the ideal voltage source with a short circuit, as shown 6 30120 = 15 A i'2 = 3 30 = 10 A i' 3 = i' 4 = 6 30 = 5 A 3 W 6 W 12 A4 W 2 W i1 " i2 " i3 " i4 " i'1 =
- 20. Thevenin's theorem Thevenin's theorem for linear electrical networks states that any combination of voltage sources, current sources, and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R. Any two-terminal, linear bilateral dc network can be replaced by an equivalent circuit consisting of a voltage source and a series resistor
- 21. Calculating the Thévenin equivalent Sequence to proper value of RTh and ETh Preliminary ◦ 1. Remove that portion of the network across which the Thévenin equation circuit is to be found. In the figure below, this requires that the load resistor RL be temporarily removed from the network.
- 22. Conclusion: ◦ 5. Draw the Thévenin equivalent circuit with the portion of the circuit previously removed replaced between the terminals of the equivalent circuit. This step is indicated by the placement of the resistor RL between the terminals of the Thévenin equivalent Insert Figure 9.26(b)
- 23. Norton theorem Norton's theorem for linear electrical networks states that any collection of voltage sources, current sources, and resistors with two terminals is electrically equivalent to an ideal current source, I, in parallel with a single resistor. Any two linear bilateral dc network can be replaced by an equivalent circuit consisting of a current and a parallel resistor.
- 24. Calculating the Norton equivalent The steps leading to the proper values of IN and RN Preliminary ◦ 1. Remove that portion of the network across which the Norton equivalent circuit is found ◦ 2. Mark the terminals of the remaining two-terminal network
- 25. Maximum power transfer theorem The maximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must be equal to the resistance of the source as viewed from the output terminals. A load will receive maximum power from a linear bilateral dc network when its total resistive value is exactly equal to the Thévenin resistance of the network as “seen” by the load RL = RTh
- 26. Resistance network which contains dependent and independent sources L 2 Th R4 V 2 L L 2 Th R2 RV pmax = = • Maximum power transfer happens when the load resistance RL is equal to the Thevenin equivalent resistance, RTh. To find the maximum power delivered to RL,
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