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. Not enough information given

Answer: (A)

Verified step by step guidance

1. Understand that the resistance of a resistor is given by the formula: $R=\frac{\rho }{L}A$, where $\rho$ is the resistivity of the material, $L$ is the length, and $A$ is the cross-sectional area.
2. Since both resistors are made of the same material and have the same cross-sectional area, the resistivity $\rho$ and $A$ are constant. Therefore, the resistance is directly proportional to the length of the resistor.
3. Let the resistance of the shorter resistor be $R$. Then, the resistance of the longer resistor, which is twice as long, will be $2R$.
4. Using Ohm's Law, $V=IR$, where $V$ is the potential difference, $I$ is the current, and $R$ is the resistance. Since the potential difference is the same for both resistors, we have $I$₁R = I₂2R.
5. Substitute the given current for the shorter resistor, $I$₁ = 5 A, into the equation to find the current through the longer resistor: $5R=I$₂2R. Solve for $I$₂.