What is the equivalent resistance between points a and b when R = 12
Ω
?

Input Answer in Ohms

Question

What is the equivalent resistance between points a and b when R = 12 
Ω
 ?

Input Answer in Ohms

BlackTom AI · Accepted Answer

The diagram shows a network of resistors arranged between nodes a and b, with a central connection forming a direct link between the top and bottom rails at the middle of the network. When a conductor (a short) directly connects two nodes in a network, it forces those two nodes to have the same electric potential, effectively bypassing any resistors that lie between them.

In this circuit, the central vertical connection creates a short between the node immediately to the left of the central vertical line (on the top rail) and the corresponding node on the bottom rail. Because these two nodes are now at the same potential, current can flow through the zero-impedance short rather than through the surrounding resistors. As a result, the path of least resistance from a to b is the central short, making the equivalent resistance between a and b equal to zero, regardless of the resistor value R (here R = 12 Ω).

Conceptually, you can think of it as the short creating a direct wire connection that bypasses the entire resistor network between a and b. In a network with an ideal short in parallel with resistors, the short dominates and the overall resistance becomes 0 Ω.

If one were to analyze the network without the short, you would have a nonzero equivalent resistance determined by the arrangement and values of the resistors. However, with the central short present, that nonzero contribution is irrelevant because the short provides a path of zero resistance across a and b.

Thus, the equivalent resistance between points a and b is 0 Ω.

PHYS-222-30000 Chapter 21 -Current and Direct Current Circuits Test

What is the equivalent resistance between points a and b when R = 12 Ω ? Input Answer in Ohms

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