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What happens to the total circuit resistance as additional branches are added to a parallel circuit?

  1. It remains the same

  2. It increases

  3. It decreases

  4. It becomes infinite

The correct answer is: It decreases

In a parallel circuit, the total circuit resistance decreases as additional branches are added. This occurs because each new branch provides an additional path for current to flow. When a resistor is added in parallel, it contributes to the total current while the voltage across all branches remains the same. According to the formula for calculating total resistance in a parallel circuit, the total resistance (R_total) is found using the equation: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ... As more resistors are added (R2, R3, etc.), the overall value of the fraction 1/R_total becomes larger, leading to a decrease in total resistance. This is a fundamental principle of parallel circuits. Each additional branch effectively lowers the overall resistance because it divides the total current through more paths, allowing more current to flow for the same voltage, hence reducing resistance.