Resistance Physics Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
A wire has resistance R=ρLAR = \rho \frac{L}{A}. If you replace a wire with one that is twice as long and has three times the cross-sectional area (same material), how does the resistance change?

Solution

  1. 1
    Original: R=ρLAR = \rho \frac{L}{A}.
  2. 2
    New wire: R′=ρ2L3A=23⋅ρLA=23RR' = \rho \frac{2L}{3A} = \frac{2}{3} \cdot \rho \frac{L}{A} = \frac{2}{3}R.

Answer

R′=23R(resistance decreases to two-thirds)R' = \frac{2}{3}R \quad (\text{resistance decreases to two-thirds})
Resistance is proportional to length (longer wire = more resistance) and inversely proportional to area (thicker wire = less resistance). Doubling length doubles R, tripling area divides R by 3.

About Resistance

A measure of how strongly a material opposes electric current, measured in ohms (Ω\Omega) — higher resistance means less current for a given voltage.

Learn more about Resistance →

More Resistance Examples

Example 1 easy

A resistor carries [formula] of current when [formula] is applied across it. What is the resistance?

Example 2 medium

A wire has length [formula], cross-sectional area [formula], and resistivity [formula] (copper). Wha

Example 3 easy

If the resistance of a wire doubles and the voltage stays the same, what happens to the current?

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