In the circuit shown in the figure,four identical resistors labeled A to D are connected to a battery as shown.S₁ and S₂ are switches.Which of the following actions would result in the GREATEST amount of current through resistor A? A) closing both switches B) closing S₁ only C) closing S₂ only D) leaving both switches open as shown.

Question

Quizplus · Accepted Answer

Closing both switches would result in the greatest amount of current through resistor A because it would create the least amount of resistance in the circuit. When both switches are closed, resistors B and C are in parallel, so their effective resistance is half of the resistance of a single resistor. This parallel combination is then in series with the other two identical resistors, resulting in a total resistance of 1.5 times the resistance of a single resistor. When only one switch is closed, the effective resistance in the circuit is greater than when both switches are closed. Therefore, closing both switches would result in the greatest amount of current through resistor A.

In the Circuit Shown in the Figure,four Identical Resistors Labeled