Question

Через 5 мин. в нагревателе, который сделан из нихромовой проволоки длиной 10 м и площадью поперечного сечения 1 мм² выделилось 2 кДж теплоты. Определите силу тока в нагревателе.

Answer 1

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Answer 2

Calculation of Current in the Heater

To determine the current in the heater, we can use the formula for electrical power:

Power (P) = Current (I) x Voltage (V)

In this case, we are given the power (2 kJ) and the length (10 m) and cross-sectional area (1 mm²) of the heater made of nichrome wire. However, we need to find the current (I).

To find the voltage, we can use Ohm's Law:

Voltage (V) = Resistance (R) x Current (I)

The resistance of the heater can be calculated using the formula:

Resistance (R) = Resistivity (ρ) x Length (L) / Cross-sectional Area (A)

The resistivity of nichrome wire is typically around 1.10 x 10^-6 Ω·m.

Let's calculate the current step by step:

1. Calculate the resistance of the heater: - Resistivity (ρ) = 1.10 x 10^-6 Ω·m - Length (L) = 10 m - Cross-sectional Area (A) = 1 mm² = 1 x 10^-6 m²

Resistance (R) = (1.10 x 10^-6 Ω·m) x (10 m) / (1 x 10^-6 m²) = 11 Ω

2. Calculate the voltage: - Voltage (V) = Power (P) / Current (I)

Since we don't know the current yet, we'll use a variable (I) for now.

3. Substitute the resistance and voltage into Ohm's Law to find the current: - Voltage (V) = Resistance (R) x Current (I)

Voltage (V) = 11 Ω x I

4. Substitute the power and voltage into the power formula to solve for the current: - Power (P) = Current (I) x Voltage (V)

2 kJ = I x (11 Ω x I)

Simplifying the equation: - 2 kJ = 11 Ω x I² - 2 kJ = 11 Ω x I² - I² = (2 kJ) / (11 Ω) - I² = (2 x 10³ J) / (11 Ω) - I² = 181.82 A² - I ≈ √181.82 A - I ≈ 13.49 A

Therefore, the current in the heater is approximately 13.49 A.

Please note that the calculations provided here are based on the given information and assumptions about the properties of nichrome wire.