Question:

Published on: 1 October, 2023

**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)

(c) (d)

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 I_{1} through the 20 Ω resistance due to the current source 1 Amp and voltage source 32 V is removed.

I_{1}=1×8/30=8/30 Amp.

The current I_{2} through the 20 Ω resistance due to the voltage source 32 V and current source 1 Amp. is removed.

I_{2}=32/30 Amp.

The total current through the resistance 20 Ω is I=I_{1}-I_{2}=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.

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