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Question:

Published on: 3 December, 2024

State and explain Thevenins theorem. Find the Thevenins equivalent of the circuit of Fig.18(a) as shown at terminal XY.

Fig. 18(a)

Answer:

Thevenin’s theorem states that any two terminal bilateral linear d.c circuits can be replaced by an equivalent circuit consisting of a voltage source and a series resistor.

Explanation:

Let us consider simple d.c. circuit as shown in Fig.17 (a), we are to find I_L by Thevenin's theorem. In order to find the equivalent voltage source, r_L is removed and V_o.c is calculated as shown in Fig. 17(b).

(a) (b)

Fig. 17(a) Simplified d.c. circuit, (b) Finding of V_o.c, Finding of R_th and (d) Finding of I_L forming Thevenin’s equivalent circuit.

Next, to find the internal resistance of the network (Thjevenin’s resistance or equivalent resistance) in series with V_o.c, the voltage source is removed (de active) by a short circuit (as the source does not have any internal resistance) as shown in Fig .17(c).

(b) (c)

(d)

Fig. 18 (b) Finding of V_o.c, (c) Finding of R_th and (d) Finding of I_L forming Thevenin’s equivalent circuit.

The current I₁ through the 20 Ω resistance due to the current source 1 Amp and voltage source 32 V is removed.

I₁=1×8/30=8/30 Amp.

The current I₂ through the 20 Ω resistance due to the voltage source 32 V and current source 1 Amp. is removed.

I₂=32/30 Amp.

The total current through the resistance 20 Ω is I=I₁-I₂=0.27-1.07=-0.8 Amp.

The current is following upward direction through the 20 Ω resistor.

The voltage drop between terminal X and Y is the open circuit voltage

V_o.c=32-20×0.8=32-16=16 V

Thevenin’s equivalent resistance R_th=(10×20)/(10+20)=6.67 Ω

The load current I_L=V_o.c/(R_th+R)=16/(6.67+R) Amp.

Subjects

Power Electronics Analog Communication Electrical Engineering Management Radio Frequency and Microwave Engineering Basic Electrical Engineering

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