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To solve for the output voltage \( V_o \) in the given circuit, we can follow these steps:

### Given:
- \( V_1 = 12 \text{ V} \)
- \( R_{\text{POT}} = 20 \text{ k}\Omega \) (total resistance of the potentiometer)
- \( R_{\text{procent}} = 55\% \) (percentage of \( R_{\text{POT}} \) between pins 1 and 2)
- \( R_1 = 56 \text{ k}\Omega \)

### Step 1: Calculate the resistance between pins 1 and 2 of the potentiometer
The resistance between pins 1 and 2, denoted \( R_2 \), is given by:

\[
R_2 = R_{\text{POT}} \times \frac{R_{\text{procent}}}{100} = 20 \text{ k}\Omega \times \frac{55}{100} = 11 \text{ k}\Omega
\]

### Step 2: Calculate the total resistance seen by the source \( V_1 \)
The total resistance \( R_T \) in the circuit is the series combination of \( R_2 \) and \( R_1 \):

\[
R_T = R_2 + R_1 = 11 \text{ k}\Omega + 56 \text{ k}\Omega = 67 \text{ k}\Omega
\]

### Step 3: Calculate the current through the circuit
Using Ohm's Law, the current \( I \) through the circuit is:

\[
I = \frac{V_1}{R_T} = \frac{12 \text{ V}}{67 \text{ k}\Omega} \approx 0.179 \text{ mA}
\]

### Step 4: Calculate the voltage drop across \( R_1 \) (which is \( V_o \))
Since \( V_o \) is the voltage across \( R_1 \), we use Ohm's Law again:

\[
V_o = I \times R_1 = 0.179 \text{ mA} \times 56 \text{ k}\Omega \approx 10.024 \text{ V}
\]

Thus, the output voltage \( V_o \) is approximately **10.024 V**.

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Do you have any questions, or would you like a more detailed explanation? Here are some related questions you might be interested in:

1. How would the output voltage change if \( R_{\text{procent}} \) were different?
2. What if \( R_1 \) was reduced to 10 kΩ—how would that affect \( V_o \)?
3. Can you explain how the potentiometer setting affects the circuit?
4. How would the output voltage change if \( V_1 \) was increased?
5. What is the power dissipated by \( R_1 \) in this configuration?

**Tip:** Remember that the position of the potentiometer's wiper (indicated by \( R_{\text{procent}} \)) directly influences the division of voltage in the circuit.

Beregn udgangsspændingen Vo: V1 = 12, RPOT = 20, Procent = 55%, R1 = 56. Calculate the output voltage Vo given the values of V1, RPOT, the percentage setting of the potentiometer, and R1.

Step-by-step guide on calculating the output voltage Vo in a series circuit including a potentiometer set at 55%. The problem involves using Ohm's Law to find the current and the voltage drop across a resistor, suitable for electrical engineering students.

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