Lecture-4

Md.Kausher ahmedElectrical department

Electrical engineering-1Code-6723

Lesson declared

The venin's theorem

After, previous class………….

Importance of Thevenin’s theorem:

• In circuit analysis Thevenin’s theorem is very important. It is helpful simplifying a circuit. A large circuit can be replaced with an independent voltage source and a resistor. This replacement system is very helpful tool in circuit design.

• According to Thevenin’s theorem we replace a huge circuit with Thevenin’s equivalent, actually original circuit behaves same as Thevenin’s equivalent.

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Consider a linear two terminal circuit shown in figure 4(a).

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• Let us find that what will make two circuits are equivalent. If we remove the load from figure 1(a), the voltage source will be open circuit then voltage source of figure 1(a) must equal to voltage source VTh in figure 1(b). So the two circuits will become equivalent and open circuit voltage across two terminals is

VTh = Voc

Fig :Thevenin’s theorem

And figure 2(a) shows that

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• Load current IL and voltage across the load vL

can be easily determined if the Thevenin’s equivalent circuit at the load terminals is obtained shown in figure 4(b).

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Thevenin’s theorem problem:

Find the Thevenin’s equivalent circuit of the circuit shown in figure 5, to the left of the terminals a-b. Then find the current through RL = 6, 16, 36Ω.

Answer

• Turning off voltage source and making short circuit and 2A current circuit replacing it open circuit we get the circuit shown in figure 6 (a)

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• To find VTh applying mesh analysis consider figure 6(b).

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• In two loops applying mesh analysis we get,• -32 + 4i1 + 12 (i1 – i2) = 0, i2 = -2A

• • i1 = 0.5A.

• • In this way VTh = 12 (i1 – i2) = 30v

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We can use alternative way nodal analysis or source transformation to find VTh. The Thevenin’s equivalent circuit shown in figure 7.

• We know• IL = VTh / (RTh + RL) = 30 / (4 + RL)

• When RL = 6, IL = 30/10 = 3A

• When RL = 16, IL = 30/20 = 1.5A

• When RL = 36, IL = 30/40 = 0.75A

Feedback

• # Explain Thevenin’s theorem.• Find the Thevenin’s equivalent circuit of the

circuit shown in figure 5, to the left of the terminals a-b. Then find the current through RL = 6, 16, 36Ω.