If the resistance of an aluminum wire at room temperature (20°C) is 100 ohm, at what temperature will its resistance increase to 120 ohm?

Answer 1

To solve this problem, we can use the formula for calculating the temperature coefficient of resistance (α) for aluminum:

Rt = Ro * (1 + α * (t - To))

where:
- Rt is the resistance at temperature t
- Ro is the resistance at the reference temperature To
- α is the temperature coefficient of resistance for aluminum

To find the temperature at which the resistance increases to 120 ohm, we will set Rt = 120 ohm, Ro = 100 ohm, and solve for t.

120 = 100 * (1 + α * (t - 20))

Dividing both sides of the equation by 100:

1.2 = 1 + α * (t - 20)

Rearranging the equation:

α * (t - 20) = 1.2 - 1

α * (t - 20) = 0.2

Now, we need to find the temperature coefficient of resistance (α) for aluminum. The temperature coefficient of resistance, α, is typically given in units of ohm per degree Celsius (Ω/°C). For aluminum, the average temperature coefficient of resistance is approximately 0.0039 Ω/°C.

So, α = 0.0039 Ω/°C.

0.0039 * (t - 20) = 0.2

Dividing both sides of the equation by 0.0039:

t - 20 = 0.2 / 0.0039

t - 20 = 51.28

Adding 20 to both sides of the equation:

t = 51.28 + 20

t ≈ 71.28

Therefore, the resistance of the aluminum wire will increase to 120 ohm at a temperature of approximately 71.28°C.