A machine part has a resistor X protruding from an opening in the side. This resistor is connected to three other resistors, as shown in Fig. E26.2. An ohmmeter connected across a and b reads 2.00 Ω. What is the resistance of X?

Short Answer

Expert verified

The resistance of X is 7.5 Ω.

Step by step solution

01

Definition of resistance

The resistance that is measured by the ohmmeter represents the equivalent resistance of the total resistors because these four resistors are connected in parallel.

Therefore, use an equation that represents the connection of the resistors in parallel as:

1Req=1R1+1R2+1R3+1Rx1Rx=1Req-1R1+1R2+1R3

02

Resistance of X

Substitute to get Rx as:

1Rx=1Req-1R1+1R2+1R3=12Ω-115Ω-15Ω-110Ω=215Rx=152Ω

The resistance of X is 7.5Ω .

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