In a parallel circuit with three equal resistors across a constant source, the total resistance equals

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Enhance your understanding of the fundamentals of electricity with the AMT General Exam. Study with multiple-choice questions crafted to improve your knowledge and confidence. Prepare effectively for your success!

Multiple Choice

In a parallel circuit with three equal resistors across a constant source, the total resistance equals

Explanation:
When resistors are in parallel, the total resistance is found by adding the reciprocals of each resistance: 1/R_total = 1/R1 + 1/R2 + 1/R3. If all three resistors are equal to R, then 1/R_total = 1/R + 1/R + 1/R = 3/R, so R_total = R/3. Another way to see it is that with the same voltage across the parallel network, each resistor draws current V/R, and the currents add: I_total = 3V/R. The equivalent resistance is R_total = V/I_total = V/(3V/R) = R/3. This reflects the idea that adding parallel paths lowers the overall resistance.

When resistors are in parallel, the total resistance is found by adding the reciprocals of each resistance: 1/R_total = 1/R1 + 1/R2 + 1/R3. If all three resistors are equal to R, then 1/R_total = 1/R + 1/R + 1/R = 3/R, so R_total = R/3.

Another way to see it is that with the same voltage across the parallel network, each resistor draws current V/R, and the currents add: I_total = 3V/R. The equivalent resistance is R_total = V/I_total = V/(3V/R) = R/3. This reflects the idea that adding parallel paths lowers the overall resistance.

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