Question

Лампа сопротивлением 2Ом соединена параллельно с двумя резисторами сопротивлением 5Ом и 15Ом , которые соединены последовательно.Найти общее сопротивление участка цепи.

Answer 1

Дано:
R1 = 2 Ом
R2 = 5 Ом
R3 = 15 Ом

R - ?

Резисторы R2 и R3 соединены ПОСЛЕДОВАТЕЛЬНО, поэтому:
R23 = R2 + R3 = 5 + 15 = 20 Ом

Лампа и резистор R23 Соединены параллельно, поэтому:
R = R1*R23 / (R1 + R23) = 2*20 / (2 + 20) ≈ 1,8 Ом

Ответ: Общее сопротивление участка 1,8 Ом

Answer 2

Calculation of Total Resistance

To find the total resistance of the circuit, we need to consider the resistors connected in parallel and in series.

Given: - Lamp resistance: 2 Ω - Two resistors connected in series with resistances of 5 Ω and 15 Ω

Step 1: Calculate the equivalent resistance of the two resistors connected in series.

When resistors are connected in series, the total resistance is the sum of the individual resistances.

Total resistance of the two resistors connected in series: R_series = 5 Ω + 15 Ω = 20 Ω

Step 2: Calculate the equivalent resistance of the lamp and the two resistors connected in series.

When resistors are connected in parallel, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances.

Let R_parallel be the equivalent resistance of the lamp and the two resistors connected in series.

1/R_parallel = 1/2 Ω + 1/20 Ω

To simplify the calculation, we can find the least common multiple (LCM) of 2 and 20, which is 20.

1/R_parallel = 10/20 Ω + 1/20 Ω = 11/20 Ω

Taking the reciprocal of both sides:

R_parallel = 20/11 Ω

Step 3: The total resistance of the circuit is equal to the equivalent resistance of the lamp and the two resistors connected in series.

Total resistance = R_parallel = 20/11 Ω

Therefore, the total resistance of the circuit is 20/11 Ω.