In the circuit shown in the figure,the resistor R has a variable resistance.As R is decreased,what happens to the currents? A)I₁ remains unchanged and I₂ increases. B)I₁ decreases and I₂ decreases. C)I₁ decreases and I₂ increases. D)I₁ increases and I₂ decreases. E)I₁ increases and I₂ increases.

Question

Quizplus · Accepted Answer

According to Kirchhoff's Current Law (KCL), the sum of currents entering a node must equal the sum of currents leaving the node. Therefore, at the node between resistors R and 2R, the current I₁ is equal to the sum of currents through resistors R and 2R, i.e. I₁ = I₂ + I₂. If R decreases, its resistance decreases and therefore its current increases for the same voltage across it. This means that I₂ must increase to compensate for the decrease in R. However, since I₁ is equal to the sum of currents through R and 2R, it must decrease to maintain KCL at the node. Therefore, the correct answer is C: I₁ decreases and I₂ increases.

In the Circuit Shown in the Figure,the Resistor R Has