How many 300 W lamps are designed for

Let us assume that the number of 300 W lamps that can be installed in parallel in a building depends on the total power of the lamps and on the amount of current that flows through the wires. To determine the maximum number of lamps, it is necessary to calculate the total power of all lamps and compare it with the power that the wiring can withstand.

First, let's calculate the total power of all lamps. Let N be the number of lamps. Then the total power will be equal to 300*N W.

Next, we will find the current that flows through the wires. To do this, we use Ohm's law: I=U/R, where I is current, U is voltage, R is conductor resistance. For a copper conductor with a cross section of 9 mm^2, the resistance can be found using special tables. To find the current, it is necessary to take into account that the voltage in the main line is 122 V, and the voltage on the lamps is 110 V.

Thus, the maximum number of lamps can be determined by the formula: N = (122-110)RI/(300*110), where R is the conductor resistance in Ohms per 100 meters, I is the maximum current that can flow through the wires.

Substituting the values, we get: N = (122-110)0.0129/(300*110) ≈ 4 lamps.

Thus, it is possible to install in parallel no more than 4 lamps with a power of 300 W in a building, if the wiring from the main line is made of copper wire 100 m long and with a cross-section of 9 mm^2, and the voltage in the main line is 122 V.

This problem is solved using Ohm's law and a formula for calculating the power of an electrical circuit.

From the problem conditions it is known that the power of one lamp is 300 W, and the voltage in the main line is 122 V. The voltage on the lamps is 110 V.

To determine the maximum number of lamps, it is necessary to calculate the total power of all lamps and compare it with the power that the wiring can withstand. The total power of all lamps will be equal to 300*N W, where N is the number of lamps.

Next, you need to find the current that flows through the wires using Ohm's law: I = U/R, where U is the voltage, R is the resistance of the conductor. For a copper conductor with a cross section of 9 mm^2, the resistance can be found using special tables.

To find the maximum number of lamps, you can use the formula: N = (122-110)RI/(300*110), where R is the conductor resistance in Ohms per 100 meters, I is the maximum current that can flow through the wires.

Let's substitute the known values ​​into the formula: R = 0.01724 Ohm/m (for copper wire with a cross-section of 9 mm^2), I = (122-110)/R = 696.43 A. Then the maximum number of lamps will be N = (122-110)0.01724696.43/(300*110) ≈ 4 lamps.

Thus, it is possible to install in parallel no more than 4 lamps with a power of 300 W in a building, if the wiring from the main line is made of copper wire 100 m long and with a cross-section of 9 mm^2, and the voltage in the main line is 122 V.

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This problem describes a situation where it is necessary to determine the number of 300 W lamps that can be installed in parallel in a building, provided that the wiring from the main line with a length of 100 m and a cross-section of 9 mm^2 is made of copper wire, and the voltage in the main line is 122 V.

To solve this problem, it is necessary to use Ohm's law, which states: the current I flowing through a conductor is proportional to the voltage U at its ends and inversely proportional to its resistance R, i.e. I = U/R.

The resistance of a conductor can be determined by the formula R = ρ * L / S, where ρ is the resistivity of the conductor material, L is the length of the conductor, and S is its cross-section.

For a copper wire, the resistivity is ρ = 0.0175 Ohm * mm^2 / m. Substituting the known values, we get: R = 0.0175 * 100 / 9 = 0.1944 Ohm.

Thus, for each lamp with a power of 300 W and a voltage of 110 V, a current is required I = P / U = 300 / 110 = 2.727 A.

Taking into account Ohm's law and the found value of the conductor resistance, it is possible to determine the maximum number of lamps that can be installed in parallel: I = U / R * n, where n is the number of lamps. Substituting the known values, we get: n = U * S / (P * ρ * L) = 122 * 9 / (300 * 0.0175 * 100) ≈ 20.

Thus, no more than 20 300 W lamps can be installed in parallel under given conditions.

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