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(1)

Step 1:

Find the Thevinins equivalent resistance.

1.Open the load resistor.

2.Open Current Sources and Short Voltage Sources.

3.Calculate the Open Circuit Resistance. This is the Thevenin Resistance (R_TH).

Redraw the circuit :

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The two networks are similar and they are in series to each other.

Step 2:

Convert the delta network to star network.

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Resistors R_a and R_b are in parallel.

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Resultant R_tis in series with R_c.

R_eq1 = 1+ 4 = 5 $\"\"$ .

Similarly for the second network , R_eq2 = 5 $\"\"$ .

So the equivalent resistance will be R_th = 5 $\"\"$ + 5 $\"\"$ = 10 $\"\"$ .

Solution :

Thevenin Resistance is R_th = 10 $\"\"$ .

(2)

Step 1:

Find the thevinins equivalent voltage.

1.Open the load resistor.

2.Calculate the Open Circuit Voltage. This is the Thevenin Voltage (V_TH).

Redraw the circuit :

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The netwrok has two independent loops.

Find the current in each loop.

Loop 1:

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Voltage at node A :

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Step 2:

Loop 1:

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Voltage at node B :

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Step 3:

Find Thevenin Voltage (V_TH).

Thevenin Voltage V_TH= V_A+ V_B.

V_TH= -2 - 6

V_TH= -8 V.

Therefore Thevenin Voltage V_TH= - 8 V.

Solution :

Thevenin Voltage is V_TH= - 8 V.