The calculation of the total power of LED lamps is closest to

Question

There is a display screen composed of a certain type of LED lamp. Each lamp emits different colors of light under different voltages, and the working current when emitting light is about 20 mA. When the voltage is 1.4 V, it emits red light, when the voltage is 1.8 V, it emits yellow light; when the voltage is 3.2 V, it emits blue light. It is known that the area of ​​the display screen is 3 m2, and the number of lamps per m2 is 1.0×104. When all the LED lamps on the entire display screen are lit. The calculation of the total power of the LED lamp is closest to
A. 1×102 W
B. 1×103 W
C. 1×104 W
D. 1×106 W

Answer 1

Answer: B. 1×103 W.

Answer analysis: When the LED lamp emits blue light, the voltage across the two ends is U=3.2V, and the current passing through is I=20mA=0.02A, so the power of each LED lamp is P=UI=3.2V×0.02A=0.064W; the number of 1m2 lamps is 1.0×104, so the total power is: Ptotal=nP=1.0×104×0.064W=640W. It can be seen that among the four options, the closest one is option B, so B is correct, and ACD are wrong.

Answer 2

Answer: C. 1×104 W.

Answer analysis: This question mainly tests the calculation of electrical power and the estimation of order of magnitude.

First, we need to determine the power of each LED lamp under different voltages. The power calculation formula is P=UI, where U is voltage and I is current. The question gives that when the LED lamp is emitting light, its operating current is about 20mA, that is, 0.02A.

For the red LED lamp, its voltage is 1.4V, so the power of a single red LED lamp is:

P(red) =U (red) I=1.4×0.02=0.028W

For the yellow LED lamp, its voltage is 1.8V, but the question does not directly ask about the power when emitting yellow light, and because we require the total power of the entire display screen, and the display screen is not only one color of LED lamp working, so here we only need to know the power when emitting red light and blue light. However, for completeness, we can write the power expression of the yellow LED lamp:

P (yellow) =U (yellow) I=1.8×0.02=0.036W

For the blue LED lamp, its voltage is 3.2V, so the power of a single blue LED lamp is:

P (blue) =U (blue)I=3.2×0.02=0.064W

Next, we need to calculate the total power of all LED lamps on the entire display. The question gives that the area of ​​the display is 3m^2, and the number of 1m^2 lamps is 1.0 x 10^4. Therefore, the total number of LED lamps on the entire display is:

N=3×1.0×10^4 =3.0×10^4

However, the question does not clearly state what proportion of the three colors of LED lamps on the display are. To simplify the calculation, we can assume that the number of three colors of LED lamps on the display is equal (this is an approximate assumption, the actual situation may be different, but in this question we will calculate based on this). Then, the number of LED lights of each color is:

N (each) = N/3 = (3.0×10^4)/3 = 1.0×10^4

Therefore, the total power of all LED lights on the entire display is:

P (total) = N (each) × (P red + P blue ) = 1.0×10^4 × (0.028+0.064) = 1.0×10^4 × 0.092 = 920W

This result is closest to option C (1×10^4 W).

In summary, the correct answer is C.