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Two resistors are made of the same material, one twice as long as the other. If the current through the shorter resistor is 5 A, what is the current through the longer resistor if they both have the same potential difference and cross-sectional area?
A
2.5 Α
B
5.0 Α
C
10 Α
D
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Understand that the resistance of a resistor is given by the formula: , where is the resistivity of the material, is the length, and is the cross-sectional area.
Since both resistors are made of the same material and have the same cross-sectional area, the resistivity and are constant. Therefore, the resistance is directly proportional to the length of the resistor.
Let the resistance of the shorter resistor be . Then, the resistance of the longer resistor, which is twice as long, will be .
Using Ohm's Law, , where is the potential difference, is the current, and is the resistance. Since the potential difference is the same for both resistors, we have .
Substitute the given current for the shorter resistor, A, into the equation to find the current through the longer resistor: . Solve for .