Question

Электрическая цепь состоит из источника тока и реостата. Внутреннее сопротивление источника r = 2 Ом. Сопротивление реостата можно изменять в пределах от 1 Ом до 5 Ом. Максимальная мощность, выделяемая на реостате, равна 4,5 Вт. Чему равна ЭДС источника?

Answer 1

R = 2 Ом. R₁=1 Ом R₂=5 Ом. P(max)=4,5 Вт. ε - ?
Закон Ома для полной цепи
I=ε/(r+R)
Максимальная мощность достигается в том случае, когда сопротивление нагрузки равно внутреннему сопротивлению источника тока, т.е. при r=R. В нашем случае с данным реостатом это возможно.
Формула мощности в этом случае принимает вид
P=IU=I²R=ε²R/(r+R)²=ε²r/(2r)²=ε²/(4r)
ε²=4rP=4*2*4.5=36
ε=6 (В)
Ответ: 6 В

Answer 2

Electric Circuit with a Current Source and Rheostat

An electric circuit consists of a current source and a rheostat. The internal resistance of the source is 2 Ω. The resistance of the rheostat can be adjusted between 1 Ω and 5 Ω. The maximum power dissipated on the rheostat is 4.5 W. We need to find the electromotive force (EMF) of the source.

To find the EMF of the source, we can use the formula:

EMF = V + Ir

Where: - EMF is the electromotive force of the source, - V is the potential difference across the rheostat, - I is the current flowing through the circuit, and - r is the internal resistance of the source.

To find the potential difference across the rheostat, we can use the formula:

V = I * R

Where: - V is the potential difference across the rheostat, - I is the current flowing through the circuit, and - R is the resistance of the rheostat.

To find the current flowing through the circuit, we can use Ohm's Law:

I = V / (r + R)

Where: - I is the current flowing through the circuit, - V is the potential difference across the rheostat, - r is the internal resistance of the source, and - R is the resistance of the rheostat.

Now, let's calculate the EMF of the source.

Calculation:

Given: - Internal resistance of the source (r) = 2 Ω - Resistance of the rheostat (R) = 1 Ω to 5 Ω - Maximum power dissipated on the rheostat = 4.5 W

To find the EMF of the source, we need to find the potential difference across the rheostat and the current flowing through the circuit.

Let's assume the resistance of the rheostat is at its maximum value, i.e., R = 5 Ω.

Using Ohm's Law, we can find the current flowing through the circuit:

I = V / (r + R)

Substituting the values, we get:

I = V / (2 + 5) = V / 7

Now, let's find the potential difference across the rheostat:

V = I * R = (V / 7) * 5

To find the maximum power dissipated on the rheostat, we can use the formula:

P = V^2 / R

Substituting the values, we get:

4.5 = (V^2) / 5

Simplifying the equation, we get:

V^2 = 4.5 * 5 = 22.5

Taking the square root of both sides, we get:

V = √22.5 ≈ 4.74 V

Now, let's substitute the value of V in the equation for I:

I = V / 7 = 4.74 / 7 ≈ 0.678 A

Finally, let's find the EMF of the source:

EMF = V + Ir = 4.74 + (0.678 * 2) ≈ 5.10 V

Therefore, the EMF of the source is approximately 5.10 V.

Conclusion:

The electromotive force (EMF) of the source is approximately 5.10 V.