Question

Три лампы мощностью 40, 60 и 100 Вт вначале соединены последовательно, а затем параллельно. Напряжение питающей сети 220 В. Определить токи ламп и общий ток для каждого соединения.

Answer 1

Представим что включены последовательно 4 лампочки.Для каждой будет выделена какая-то часть напряжения.Допучтим что они на напряжение 220в
Тогда на каждую припадает по 55в.Найдём ток и сопротивл.:
100вт/55=1.84а     55/1.81=30.3ом        Для паралель.соединения найдём
 60вт/55=1.09а       55/1.09=50.45ом
 40/55=0.727а        55/0.727=75.6ом           Rобщ=15.12ом
Для последовательно включённых ламп их сопротивления будут такие же.,а  Rобщ=156.48ом    R=15.12+156.48=171.6ом
Общий ток  I=220/171.6=1.28a
При этом падения напряжения на 40вт лампочке будет 1.28*75.65=97.2в 
                                                         на 60вт ламп.                    1.28*50.45=64.5в
                                                        на 40 вт лампочке           1.28*30.38  = 38.8в
а на группе паралельно включённых лампочек будет 1.28*15.12= 19.35в
что в сумме составит 220в.
Токи : в 100вт лампочке 19.35в/30.38=0.636а
            в 60вт ламп.           19.35/50.45= 0.383а
           в 40вт лампочке     19.35/75.65=0.255а

Answer 2

Problem Statement

We have three light bulbs with power ratings of 40W, 60W, and 100W. Initially, the bulbs are connected in series, and then they are connected in parallel. The power supply voltage is 220V. We need to determine the currents flowing through each bulb and the total current for each connection.

Solution

To solve this problem, we need to apply Ohm's law and the rules for series and parallel connections of resistors.

# Series Connection

When the bulbs are connected in series, the total resistance is the sum of the individual resistances. The current flowing through the circuit can be calculated using Ohm's law: I = V / R, where I is the current, V is the voltage, and R is the resistance.

In this case, the resistance of each bulb can be calculated using the formula: R = V^2 / P, where R is the resistance, V is the voltage, and P is the power.

Let's calculate the currents for the series connection:

1. Calculate the resistance of each bulb: - For the 40W bulb: R1 = (220^2) / 40 - For the 60W bulb: R2 = (220^2) / 60 - For the 100W bulb: R3 = (220^2) / 100

2. Calculate the total resistance: RTotal = R1 + R2 + R3

3. Calculate the total current: ITotal = V / RTotal

4. Calculate the current through each bulb: - For the 40W bulb: I1 = V / R1 - For the 60W bulb: I2 = V / R2 - For the 100W bulb: I3 = V / R3

# Parallel Connection

When the bulbs are connected in parallel, the voltage across each bulb is the same, and the total current is the sum of the individual currents.

Let's calculate the currents for the parallel connection:

1. Calculate the current through each bulb: - For the 40W bulb: I1 = V / R1 - For the 60W bulb: I2 = V / R2 - For the 100W bulb: I3 = V / R3

2. Calculate the total current: ITotal = I1 + I2 + I3

Calculation

Now, let's calculate the currents for both the series and parallel connections.

# Series Connection:

- Resistance of the 40W bulb: R1 = (220^2) / 40 - Resistance of the 60W bulb: R2 = (220^2) / 60 - Resistance of the 100W bulb: R3 = (220^2) / 100

- Total resistance: RTotal = R1 + R2 + R3 - Total current: ITotal = V / RTotal

- Current through the 40W bulb: I1 = V / R1 - Current through the 60W bulb: I2 = V / R2 - Current through the 100W bulb: I3 = V / R3

# Parallel Connection:

- Current through the 40W bulb: I1 = V / R1 - Current through the 60W bulb: I2 = V / R2 - Current through the 100W bulb: I3 = V / R3

- Total current: ITotal = I1 + I2 + I3

Calculation Results

Using the given power ratings and voltage, we can calculate the currents for both the series and parallel connections.

# Series Connection:

- Resistance of the 40W bulb: R1 = (220^2) / 40 - Resistance of the 60W bulb: R2 = (220^2) / 60 - Resistance of the 100W bulb: R3 = (220^2) / 100

- Total resistance: RTotal = R1 + R2 + R3 - Total current: ITotal = 220 / RTotal

- Current through the 40W bulb: I1 = 220 / R1 - Current through the 60W bulb: I2 = 220 / R2 - Current through the 100W bulb: I3 = 220 / R3

# Parallel Connection:

- Current through the 40W bulb: I1 = 220 / R1 - Current through the 60W bulb: I2 = 220 / R2 - Current through the 100W bulb: I3 = 220 / R3

- Total current: ITotal = I1 + I2 + I3

Now, let's calculate the values using the given power ratings and voltage.