Consider the following circuit: 

The Thévenin equivalent resistance ($$Omega$$) at Points A-B is most nearly:

A.   8
B.   12
C.   20
D.   26

1 Answer

DEMETRIOS LAMBROPOULOS

Updated on December 24th, 2020

The Thévenin equivalent resistance at Points A-B can be found by shorting all voltage sources and placing open-circuits for all current sources. The circuit in question only contains a 12 V independent voltage source, so we will replace this with a short circuit. 

Once the voltage source is shorted, we can see that the 6Ω and 12Ω resistors are in parallel with each other and in series with the 8Ω resistor.

Note: Resistors in parallel are represented with two verticle lines (||) and the equivalent resistance of N resistors in parallel is calculated as follows:

R1||R2||...||RN-1||RN = 1R1+1R2+...+1RN-1+1RN-1

The Thévenin equivalent resistance can now be seen as 

RTH = 6Ω||12Ω + 8Ω          = 16+112-1 +8          = 212+112-1+ 8          = 312-1+ 8          = 4+8          = 12Ω

Therefore, we can conclude that the answer is B 12 Ω.

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