When a potential difference of 10 V is placed across a certain solid cylindrical resistor, the current through it is 2 A. If the diameter of this resistor is now tripled, what will be the new current through the resistor?

New Resistance = 0.5556 ohm

Explanation:

Resistance = resistivity * length /area

Here since resistivity and length are constant, we only need to see how the resistance increases or decreases with change in area.

New Area = pi * (3*D)^2 / 4

Old Area = pi * D^2 / 4

The ratio of new area / old area is :

Since area increases 9 times, and it is inversely proportional to resistance:

Resistance decreases by 9 times.

So, old resistance = Voltage / Current = 10 / 2 = 5 ohm

New Resistance = 5 / 9 = 0.5556 ohm    (decreases by 9 times)

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