Question

К батарейке с внутренним сопротивлением r=100 Ом присоединяют два одинаковых резистора, соединённых в первом случае последовательно, а во втором — параллельно. Оказалось, что в обоих опытах на одном резисторе выделяется одна и та же тепловая мощность. Найдите сопротивление резистора. Ответ выразите в омах, округлите до целого числа.

Answer 1

Ответ:

100 Ом

Объяснение:

Выразим токи, которые будут течь через один из резисторов в обоих случаях

$I_1=\frac{\xi}{r+2R}$

$I_2=\frac{1}{2} \frac{\xi}{r+0.5R}$

Множитель 1/2 здесь появляется из-за того, что ток разветвляется при параллельном соединении резисторов. Очевидно, что должны быть равны эти токи

$\frac{\xi}{r+2R}=\frac{1}{2} \frac{\xi}{r+0.5R}$

$r+2R=2(r+0.5R)$

$r+2R=2r+R$

$R=r=100$ Ом.

Answer 2

Problem Analysis

We are given a battery with an internal resistance of 100 Ω. Two identical resistors are connected to the battery in two different configurations: in series and in parallel. In both experiments, the same amount of thermal power is dissipated across one of the resistors. We need to find the resistance of the resistor.

Solution

Let's denote the resistance of the resistor as R.

In the first experiment, the resistors are connected in series. In a series circuit, the total resistance is the sum of the individual resistances. Therefore, the total resistance in the first experiment is R + R = 2R.

In the second experiment, the resistors are connected in parallel. In a parallel circuit, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances. Therefore, the total resistance in the second experiment is 1/R + 1/R = 2/R.

Since the same amount of thermal power is dissipated across one of the resistors in both experiments, we can equate the thermal power equations for the two experiments.

Thermal Power Equation

The thermal power dissipated across a resistor can be calculated using the formula:

P = I^2 * R

where P is the thermal power, I is the current flowing through the resistor, and R is the resistance of the resistor.

In both experiments, the thermal power is the same. Therefore, we can write:

(I^2 * R) = (I^2 * (2R))

Simplifying the equation, we get:

R = 2R

Dividing both sides of the equation by R, we get:

1 = 2

This equation is not possible, as it leads to a contradiction. Therefore, there is no valid solution for the resistance of the resistor that satisfies the given conditions.

Conclusion

Based on the given information, there is no valid solution for the resistance of the resistor that satisfies the conditions of the problem.