This problem is asking us to calculate the electromotive force (EMF or "gaya gerak listrik") of a battery in volts, using information about current and resistance.

Given dataThis problem is asking us to calculate the electromotive force (EMF or "gaya gerak listrik") of a battery in volts, using information about current and resistance.

Given

• Initial current, $I_1 = 0.6 \, \text{A}$
• Current after adding a second resistor, $I_2 = 0.5 \, \text{A}$
• Resistance of the second resistor, $R_2 = 4.0 \, \Omega$

The resistors are connected in series, which means their total resistance increases when the second resistor is added.

Step 1: Ohm's Law

We can use Ohm’s law: $V = I \times R$ Where:

• $V$ is the electromotive force (EMF) or voltage
• $I$ is the current
• $R$ is the resistance

Step 2: Determine the resistance of the first resistor

From the initial condition where the current is $0.6 \, \text{A}$, we can assume that there is one resistor (call it $R_1$) connected to the battery.

Using Ohm’s law, the EMF of the battery is: $V = I_1 \times R_1 = 0.6 \times R_1$ This equation represents the total voltage or EMF.

Step 3: Analyze the new current after adding the second resistor

When the second resistor $R_2 = 4.0 \, \Omega$ is added in series, the total resistance becomes $R_{\text{total}} = R_1 + 4.0 \, \Omega$, and the current drops to $0.5 \, \text{A}$.

Using Ohm’s law again: $V = I_2 \times R_{\text{total}} = 0.5 \times (R_1 + 4.0)$ This represents the same EMF as in the first case.

Step 4: Equate the two expressions for voltage

From both scenarios, we know the voltage must be the same: $0.6 \times R_1 = 0.5 \times (R_1 + 4.0)$

Step 5: Solve for $R_1$

Expand the equation: $0.6 R_1 = 0.5 R_1 + 2$ Now, subtract $0.5 R_1$ from both sides: $0.1 R_1 = 2$ Solve for $R_1$: $R_1 = \frac{2}{0.1} = 20 \, \Omega$

Step 6: Calculate the EMF

Now that we know $R_1 = 20 \, \Omega$, we can substitute it back into the equation for the EMF: $V = 0.6 \times 20 = 12 \, \text{V}$

Final Answer:

The EMF of the battery is 12 volts. Hence, the correct option is:

d. 12

Do you want further explanation or details on the steps? Here are some related questions for practice:

1. How would the current change if the second resistor was 6 ohms instead of 4 ohms?
2. What happens to the total resistance when resistors are added in series?
3. How is the voltage across each resistor affected in a series circuit?
4. What would be the new current if the second resistor was connected in parallel with the first?
5. Can you derive the formula for total resistance in a parallel circuit?

Tip: When resistors are added in series, the total resistance increases, reducing the current if the voltage remains constant.