(b) What is the resistance of a carbon rod at 25.8°C if its resistance is 0.0160 Ω at 0.0°C?

Verified step by step guidance

1. Understand that the resistance of a material changes with temperature. For a carbon rod, this change can be calculated using the formula for temperature dependence of resistance: R = R₀(1 + α(T - T₀)), where R is the resistance at temperature T, R₀ is the resistance at reference temperature T₀, and α is the temperature coefficient of resistance.
2. Identify the given values: R₀ = 0.0160 Ω at T₀ = 0.0°C, and the temperature T = 25.8°C. The temperature coefficient of resistance for carbon, α, is typically negative and small, around -0.0005 per °C.
3. Substitute the known values into the formula: R = 0.0160 Ω * (1 + (-0.0005)(25.8°C - 0.0°C)).
4. Calculate the change in temperature: ΔT = 25.8°C - 0.0°C = 25.8°C.
5. Use the formula to find the resistance at 25.8°C: R = 0.0160 Ω * (1 - 0.0005 * 25.8). This will give you the resistance of the carbon rod at the specified temperature.

Key Concepts

Resistance

Resistance is a measure of the opposition to the flow of electric current in a conductor. It is influenced by the material's properties, temperature, and dimensions. The unit of resistance is the ohm (Ω), and it determines how much current will flow for a given voltage.

Temperature Coefficient of Resistance

The temperature coefficient of resistance quantifies how the resistance of a material changes with temperature. For most conductors, resistance increases with temperature, and this relationship is often linear over small temperature ranges. The coefficient is specific to the material and is used to calculate resistance changes.

Linear Approximation of Resistance Change

Linear approximation assumes that resistance changes proportionally with temperature over a limited range. The formula R = R₀(1 + αΔT) is used, where R is the resistance at the new temperature, R₀ is the initial resistance, α is the temperature coefficient, and ΔT is the change in temperature. This simplifies calculations for small temperature variations.