The exercise involves determining the electromotive force (fem) $E$ and the internal resistance $r$ of a battery based on the voltage readings at its terminals for different currents.

Here’s a breakdown of the given data:

• When the current is $I_1 = 200 \, \text{mA}$, the terminal voltage is $U_1 = 4.2 \, \text{V}$.
• When the current is $I_2 = 500 \, \text{mA}$, the terminal voltage is $U_2 = 3.75 \, \text{V}$.

We can use the formula for the terminal voltage of a battery with internal resistance: $U = E - rI$ Where:

• $U$ is the terminal voltage
• $E$ is the electromotive force (fem)
• $r$ is the internal resistance
• $I$ is the current

From the two measurements, we can set up a system of two equations:

1. $4.2 = E - r(0.2)$
2. $3.75 = E - r(0.5)$

We can solve these equations to find $E$ and $r$.

Let me proceed with solving this system. sympy import symbols, Eq, solve

Define variables

E, r = symbols('E r')

Define the equations

eq1 = Eq(E - r * 0.2, 4.2) eq2 = Eq(E - r * 0.5, 3.75)

Solve the system of equations

solution = solve((eq1, eq2), (E, r)) solutionThe solution to the system of equations is:

• The electromotive force (fem), $E$, is $4.5 \, \text{V}$.
• The internal resistance, $r$, is $1.5 \, \Omega$.

For the second part of the exercise, to calculate the short-circuit current ($I_{\text{cc}}$), where the terminal voltage is zero, we can use the formula: $U = E - rI$ Setting $U = 0$ for the short-circuit condition: $0 = E - rI_{\text{cc}}$ Solving for $I_{\text{cc}}$: $I_{\text{cc}} = \frac{E}{r}$

Let's calculate that now. Calculate the short-circuit current I_cc = solution[E] / solution[r] I_ccThe short-circuit current ($I_{\text{cc}}$) is $3.0 \, \text{A}$.

Would you like further details or clarification on any part of this calculation? Here are some related questions:

1. How does the internal resistance affect the performance of the battery in a circuit?
2. What would happen to the terminal voltage if the current were even higher?
3. How can we determine the efficiency of a battery based on these measurements?
4. What is the impact of a very low internal resistance on battery life?
5. How do we calculate the power dissipated in the internal resistance?

Tip: When calculating the short-circuit current, remember that it assumes zero terminal voltage, which typically happens when a battery is directly connected to a low-resistance load.