Question

Лампу накаливания мощностью 60 Вт, рассчитанную на напряжение 120 В. необходимо включить в сеть напряжением 220 В. Какое добавочное сопротивление надо последовательно соединить с лампой, чтобы она давала нормальный накал? Какой длины нихромо вый проводник потребуется для изготовления этого сопротивления при поперечном сечении 0,20 мм2?​

Answer 1

Ответ:

Объяснение:

Нормальный ток, который должен течь через лампу равен:
I = W / U = 60 / 120 = 0.5 A
Добавочное сопротивление должно гасить лишнее напряжение в 220 - 120 = 100 В. при токе 0.5 А значение сопротивления составит:
R = U / I = 100 / 0.5 = 200 Ом.
Сопротивление проводника рассчитывается по формуле:
R = p * l / S
Выразим отсюда длину проводника:
l = R * S / p
Нихромовый проводник имеет удельное сопротивление 1.1 Ом * мм² / м
Подставляем:
l = 200 * 0.20 / 1.1 = 36.36м

Answer 2

Calculation of Additional Resistance

To calculate the additional resistance that needs to be connected in series with the 60W incandescent lamp to make it work properly with a voltage of 220V, we can use Ohm's Law. Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance.

The power of the lamp is given as 60W, and the voltage it is designed for is 120V. We can calculate the resistance of the lamp using the formula:

Resistance (R) = (Voltage (V)^2) / Power (P)

Substituting the given values:

Resistance (R) = (120V^2) / 60W = 240Ω.

To find the additional resistance required to make the lamp work with a voltage of 220V, we can subtract the resistance of the lamp from the total resistance required:

Additional Resistance = Total Resistance - Resistance of the Lamp

Total Resistance = (Voltage (V)^2) / Power (P) = (220V^2) / 60W = 806.67Ω

Additional Resistance = 806.67Ω - 240Ω = 566.67Ω

Therefore, an additional resistance of approximately 566.67Ω needs to be connected in series with the lamp to make it work properly with a voltage of 220V.

Calculation of Length of Nichrome Wire

To calculate the length of the nichrome wire required to create this resistance, we need to know the resistivity of the wire material and the cross-sectional area of the wire.

The resistivity of nichrome wire is typically around 1.10 x 10^-6 Ω·m However, the cross-sectional area of the wire is given as 0.20 mm^2.

To calculate the length of the wire, we can use the formula:

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

Rearranging the formula to solve for length:

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

Substituting the given values:

Length (L) = (566.67Ω x 0.20 x 10^-6 m^2) / (1.10 x 10^-6 Ω·m) = 1.03 meters

Therefore, a nichrome wire with a length of approximately 1.03 meters and a cross-sectional area of 0.20 mm^2 would be required to create the additional resistance needed for the lamp.

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