Question

a circuit has a current of 2.4 a. the voltage is increased to 4 times its original value, while the resistance stays the same. how should the resistance change to return the current to its original value if the voltage remains at its increased amount? it should decrease to one - half of its value. it should decrease to one - fourth of its value. it should increase to two times its value. it should increase to four times its value.

Explanation:

Step1: Recall Ohm's Law

$V = IR$, where $V$ is voltage, $I$ is current and $R$ is resistance.

Step2: Analyze the first - change

Let the original voltage be $V_1$, current be $I_1$ and resistance be $R_1$. So $V_1=I_1R_1$. The new voltage $V_2 = 4V_1$ and $R_2=R_1$. Then $V_2=I_2R_2$, substituting $V_2 = 4V_1$ and $R_2 = R_1$ gives $4V_1=I_2R_1$. Since $V_1=I_1R_1$, we have $I_2 = 4I_1$.

Step3: Analyze the second - change

We want to return $I$ to $I_1$ while $V$ remains at $V_2 = 4V_1$. Let the new - new resistance be $R_3$. Using $V_2=I_1R_3$, and since $V_2 = 4V_1$ and $V_1=I_1R_1$, we have $4V_1=I_1R_3$. Substituting $V_1=I_1R_1$ into $4V_1=I_1R_3$ gives $4I_1R_1=I_1R_3$, so $R_3 = 4R_1$. The resistance should increase to four times its value.

Answer:

It should increase to four times its value.