Open Question
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?
27. Resistors & DC Circuits
Combining Resistors in Series & Parallel
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What is the equivalent resistance of the following combination of resistors?
A
0.69 Ω
B
1.45 Ω
C
5.8 Ω
D
6.2 Ω
Verified step by step guidance1
First, identify the configuration of the resistors in the circuit. Notice that the 2 Ω and 3 Ω resistors are in parallel, while the 1 Ω and 4 Ω resistors are in series with the parallel combination.
Calculate the equivalent resistance of the parallel resistors (2 Ω and 3 Ω) using the formula for parallel resistors: 1/R_parallel = 1/R1 + 1/R2. Substitute R1 = 2 Ω and R2 = 3 Ω into the formula.
After finding the equivalent resistance of the parallel combination, add it to the series resistors (1 Ω and 4 Ω) to find the total equivalent resistance of the circuit. Use the formula for series resistors: R_total = R_series1 + R_series2 + R_parallel.
Substitute the values of the series resistors and the calculated parallel resistance into the series formula to find the total equivalent resistance.
Review the calculations to ensure accuracy and verify that the total equivalent resistance matches the expected value of 6.2 Ω.
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