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

Original current: $I = \frac{V}{R} = 2.4\,\text{A}$
New voltage: $V' = 4V$ (resistance unchanged first)
New current: $I' = \frac{V'}{R} = \frac{4V}{R} = 4I$

Step2: Adjust resistance to restore original current

Keep $V' = 4V$, want $I'' = I$.
From $I'' = \frac{V'}{R''}$, substitute values:
$I = \frac{4V}{R''}$
Since $I = \frac{V}{R}$, substitute:
$\frac{V}{R} = \frac{4V}{R''}$
Cancel $V$: $\frac{1}{R} = \frac{4}{R''}$ → $R'' = 4R$

Answer:

It should increase to four times its value.