Question

Два одинаковых резистора, сопротивление которых по R1=R2=10 Ом, подключены к источнику тока. Мощность P, которая выделяется во внешней цепи, равна 20 Вт и одинакова при последовательном и параллельном соединениях резисторов. ЭДС источника тока равна?

Answer 1

(последовательное  соединение)
I=ЭДС/(2R+r)
U=I*2R=ЭДС*2R/(2R+r)
P=I*U=ЭДС^2*2R/(2R+r)^2

(параллельное  соединение)
I=ЭДС/(R/2+r)
U=I*R/2=ЭДС*(R/2)/(R/2+r)
P=I*U=ЭДС^2*(R/2)/(R/2+r)^2

по условию задачи
P=ЭДС^2*2R/(2R+r)^2=ЭДС^2*(R/2)/(R/2+r)^2
2R/(2R+r)^2=(R/2)/(R/2+r)^2
4=((2R+r)/(R/2+r))^2
2=(2R+r)/(R/2+r)
R+2r=2R+r
r=R

P=ЭДС^2*2R/(2R+r)^2=ЭДС^2*2R/(2R+R)^2=ЭДС^2*2/(9R)
ЭДС=корень( P*9*R/2) = корень( 20*9*10/2) = 30 В - это ответ

Answer 2

Calculating the EMF of the Current Source

To calculate the electromotive force (EMF) of the current source, we can use the given information about the power dissipated in the external circuit when the resistors are connected in both series and parallel.

Given: - Resistance of each resistor, R1 = R2 = 10 Ω - Power dissipated in the external circuit, P = 20 W

We can start by calculating the equivalent resistance for both the series and parallel connections of the resistors.

Calculating Equivalent Resistance for Series Connection

The equivalent resistance for resistors connected in series is given by the sum of individual resistances: R = R1 + R2 Substituting the given values: R = 10 Ω + 10 Ω = 20 Ω

Calculating Equivalent Resistance for Parallel Connection

The equivalent resistance for resistors connected in parallel is given by the reciprocal of the sum of the reciprocals of individual resistances: 1/R = 1/R1 + 1/R2 Substituting the given values: 1/R = 1/10 Ω + 1/10 Ω = 1/5 Ω R = 5 Ω

Calculating the EMF of the Current Source

Now, we can use the power dissipated in the external circuit to calculate the EMF of the current source for both the series and parallel connections.

For a series connection, the power dissipated in the external circuit is given by: P = I^2 * R Where I is the current and R is the equivalent resistance.

For a parallel connection, the power dissipated in the external circuit is also given by: P = I^2 * R Where I is the current and R is the equivalent resistance.

Since the power dissipated in the external circuit is the same for both connections, we can equate the expressions for power in terms of current and resistance for both series and parallel connections and solve for the current.

Solving for the Current

For both series and parallel connections, the power equation can be written as: P = I^2 * R Solving for the current (I): I = sqrt(P / R)

Substituting the given power (P = 20 W) and the calculated equivalent resistances (R_series = 20 Ω, R_parallel = 5 Ω), we can solve for the current in both cases.

Calculating EMF

Finally, once the current is calculated, the electromotive force (EMF) of the current source can be determined using Ohm's law: EMF = I * R

By following these steps, the EMF of the current source can be calculated for both the series and parallel connections of the resistors.