Question

Семь одинаковых ламп последовательно включены в сеть напряжением 42 В. Мощность каждой из ламп 20 Вт. На сколько изменится общая мощность тока, если одну из ламп заменить лампой с надписью "9 В, 15 Вт"?

Answer 1

В первом случае общая мощность равна суммарной мощности всех ламп. Во втором же случае, найдем для начала ток, текущий в цепи. P=UI; I=1.67; Найдем общую мощность во второй цепи. P2=UoI=70, поэтому мощность уменьшится в два раза, то есть на семьдесят ватт

Answer 2

Calculation of Total Power and Current

To calculate the change in total power and current when one of the lamps is replaced, we need to consider the following information:

- There are seven identical lamps connected in series. - The voltage across the network is 42 V. - The power of each lamp is 20 W.

To find the total power and current, we can use the formulas:

- Power (P) = Voltage (V) * Current (I) - Current (I) = Voltage (V) / Resistance (R)

Since the lamps are connected in series, the total resistance (R_total) can be calculated by summing up the resistances of each lamp:

- Resistance (R) = Voltage (V) / Current (I) - Resistance (R_total) = Resistance (R1) + Resistance (R2) + ... + Resistance (R7)

Let's calculate the initial total power and current:

- Voltage (V) = 42 V - Power of each lamp (P) = 20 W - Current (I) = Voltage (V) / Resistance (R_total)

The resistance of each lamp can be calculated using the formula:

- Resistance (R) = Voltage (V) / Current (I)

Since the power of each lamp is given as 20 W, we can calculate the resistance of each lamp using the formula:

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

Let's calculate the initial total power and current:

1. Calculate the resistance of each lamp: - Resistance (R) = (42 V)^2 / 20 W = 88.2 Ω

2. Calculate the total resistance: - Resistance (R_total) = 7 * Resistance (R) = 7 * 88.2 Ω = 617.4 Ω

3. Calculate the current: - Current (I) = Voltage (V) / Resistance (R_total) = 42 V / 617.4 Ω ≈ 0.068 A (rounded to three decimal places)

4. Calculate the initial total power: - Power (P_total) = Voltage (V) * Current (I) = 42 V * 0.068 A ≈ 2.856 W (rounded to three decimal places)

Calculation of New Total Power and Current

Now, let's calculate the new total power and current when one of the lamps is replaced with a lamp labeled "9 V, 15 W".

1. Calculate the resistance of the new lamp: - Resistance (R_new) = (9 V)^2 / 15 W = 5.4 Ω

2. Calculate the new total resistance: - Replace the resistance of one of the lamps with the resistance of the new lamp: - New total resistance (R_total_new) = 6 * Resistance (R) + Resistance (R_new) = 6 * 88.2 Ω + 5.4 Ω ≈ 534.6 Ω (rounded to one decimal place)

3. Calculate the new current: - Current (I_new) = Voltage (V) / New total resistance (R_total_new) = 42 V / 534.6 Ω ≈ 0.079 A (rounded to three decimal places)

4. Calculate the new total power: - Power (P_total_new) = Voltage (V) * New current (I_new) = 42 V * 0.079 A ≈ 3.318 W (rounded to three decimal places)

Conclusion

When one of the lamps is replaced with a lamp labeled "9 V, 15 W", the total power of the network increases from approximately 2.856 W to approximately 3.318 W, and the total current increases from approximately 0.068 A to approximately 0.079 A.

Please note that these calculations assume ideal conditions and do not take into account factors such as variations in lamp resistance or the effect of temperature on lamp performance.