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If the voltage across a fixed resistance is doubled, what happens to the current?
  1. It doubles.
  2. It halves.
  3. It stays the same.
  4. The current cannot be determine
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OpenStax College Physics for AP® Courses Solution, Chapter 20, Problem 5 (Test Prep for AP® Courses) (0:50)

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This is College Physics Answers with Shaun Dychko. Ohm's Law says voltage equals current times resistance and so we can solve this for current by dividing both sides by <i>R</i>. So we have in the first case in the first circuit, we have current one equals the voltage one divided by <i>R</i> and I did not put a subscript on the <i>R</i> because we're told that the resistance is fixed, so it's the same for both circuits. Now in circuit two, we have the voltage two divided by the same resistance <i>R</i>. But <i>V two</i> we're told is double <i>V one</i> and so I've substituted two <i>V one</i> in place of <i>V two</i>. Now we see that this part is <i>I one</i> and so <i>I two</i> is two times <i>I one</i>. So the answer is A, it doubles.