In a two-resistor parallel circuit, which expression correctly represents the relationship of total resistance?

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Study for the AAMI Certified Associate in Biomedical Technology Exam. Study with flashcards and multiple choice questions, each question has hints and explanations. Get ready for your exam!

Multiple Choice

In a two-resistor parallel circuit, which expression correctly represents the relationship of total resistance?

Explanation:
In parallel, the same voltage appears across each resistor, so the currents through them add to give the total current. Using Ohm’s law, I1 = V/R1 and I2 = V/R2, so the total current It = I1 + I2 = V(1/R1 + 1/R2). The total current is also It = V/Rt, so V/Rt = V(1/R1 + 1/R2). Canceling the voltage V gives 1/Rt = 1/R1 + 1/R2. This is the correct relationship for two resistors in parallel. You can also rearrange to Rt = (R1*R2)/(R1+R2). The other expressions would describe resistors in series or are not consistent with parallel behavior.

In parallel, the same voltage appears across each resistor, so the currents through them add to give the total current. Using Ohm’s law, I1 = V/R1 and I2 = V/R2, so the total current It = I1 + I2 = V(1/R1 + 1/R2). The total current is also It = V/Rt, so V/Rt = V(1/R1 + 1/R2). Canceling the voltage V gives 1/Rt = 1/R1 + 1/R2. This is the correct relationship for two resistors in parallel. You can also rearrange to Rt = (R1*R2)/(R1+R2). The other expressions would describe resistors in series or are not consistent with parallel behavior.

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