If the current through a conductor is doubled, what happens to the resistance if the voltage remains constant?

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Q: If the current through a conductor is doubled, what happens to the resistance if the voltage remains constant?

Solution: According to Ohm's law, V = I * R. If V is constant and I is doubled, R must halve to maintain the equation.

Steps: 8

Step 1: Understand Ohm's Law, which states that Voltage (V) equals Current (I) times Resistance (R). This can be written as V = I * R.
Step 2: Identify that in this scenario, the voltage (V) is constant, meaning it does not change.
Step 3: Recognize that if the current (I) is doubled, we can represent this as I_new = 2 * I_original.
Step 4: Substitute the new current into Ohm's Law: V = (2 * I_original) * R_new.
Step 5: Since V is constant, we can set the original equation equal to the new one: I_original * R_original = (2 * I_original) * R_new.
Step 6: Cancel I_original from both sides of the equation (assuming it's not zero): R_original = 2 * R_new.
Step 7: Rearrange the equation to find R_new: R_new = R_original / 2.
Step 8: Conclude that if the current is doubled and the voltage remains constant, the resistance must be halved.