Question

При замиканні елемента на опір 4.5 Ом струм у колі дорівнює 0.2А а при замиканні того ж самого елемента на опір 10 Ом струм у колі 0.1 А. Знайти ЕРС елемента та його внутрішній опір

Answer 1

Calculation of the EMF and Internal Resistance of the Element

To find the electromotive force (EMF) and internal resistance of the element, we can use Ohm's Law and the concept of equivalent resistance.

Let's denote the EMF of the element as E and its internal resistance as r.

According to Ohm's Law, the current (I) in a circuit is equal to the voltage (V) divided by the resistance (R):

I = V / R

In the first scenario, when the element is short-circuited on a resistance of 4.5 Ω, the current in the circuit is 0.2 A. Using Ohm's Law, we can write:

0.2 A = E / (4.5 Ω + r) ---(1)

In the second scenario, when the same element is short-circuited on a resistance of 10 Ω, the current in the circuit is 0.1 A. Again, using Ohm's Law, we can write:

0.1 A = E / (10 Ω + r) ---(2)

We now have a system of two equations with two unknowns (E and r). We can solve this system of equations to find the values of E and r.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution. Rearranging equation (1), we get:

E = 0.2 A * (4.5 Ω + r)

Substituting this expression for E into equation (2), we get:

0.1 A = (0.2 A * (4.5 Ω + r)) / (10 Ω + r)

Simplifying this equation, we have:

0.1 A = (0.9 Ω + 0.2 A * r) / (10 Ω + r)

Cross-multiplying, we get:

0.1 A * (10 Ω + r) = 0.9 Ω + 0.2 A * r

Expanding and rearranging the terms, we have:

1 A * Ω + 0.1 A * r = 0.9 Ω + 0.2 A * r

Subtracting 0.2 A * r from both sides, we get:

1 A * Ω - 0.2 A * r = 0.9 Ω

Rearranging the terms, we have:

0.8 A * Ω = 0.2 A * r

Dividing both sides by 0.2 A, we get:

4 Ω = r

Now that we have found the value of the internal resistance (r), we can substitute it back into equation (1) to find the EMF (E):

0.2 A = E / (4.5 Ω + 4 Ω)

Simplifying this equation, we have:

0.2 A = E / 8.5 Ω

Cross-multiplying, we get:

E = 0.2 A * 8.5 Ω

Calculating the value, we find:

E = 1.7 V

Therefore, the EMF of the element is 1.7 V and its internal resistance is 4 Ω.

Conclusion

The electromotive force (EMF) of the element is 1.7 V, and its internal resistance is 4 Ω. These values were calculated based on the given information about the current in the circuit when the element is short-circuited on different resistances.