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This circuit consists of resistors \( R_1 \), \( R_2 \), and \( R_3 \), where \( R_2 \) and \( R_3 \) are in parallel, and \( R_1 \) is in series with this parallel combination. We are tasked with calculating the total current \( I_{TOT} \), the branch currents \( I_1 \) and \( I_2 \), and the voltages across \( R_1 \) and the parallel combination of \( R_2 \) and \( R_3 \) (i.e., \( U_1 \) and \( U_2 \)).

### Step 1: Equivalent Resistance of \( R_2 \) and \( R_3 \) (Parallel combination)

The total resistance of two resistors in parallel, \( R_2 \) and \( R_3 \), is given by:
\[
\frac{1}{R_{\text{parallel}}} = \frac{1}{R_2} + \frac{1}{R_3}
\]
Substituting the given values of \( R_2 = 200 \, \Omega \) and \( R_3 = 200 \, \Omega \):
\[
\frac{1}{R_{\text{parallel}}} = \frac{1}{200} + \frac{1}{200} = \frac{2}{200} = \frac{1}{100}
\]
Thus, 
\[
R_{\text{parallel}} = 100 \, \Omega
\]

### Step 2: Total Resistance of the Circuit

Since \( R_1 = 1000 \, \Omega \) is in series with \( R_{\text{parallel}} = 100 \, \Omega \), the total resistance \( R_{\text{total}} \) is:
\[
R_{\text{total}} = R_1 + R_{\text{parallel}} = 1000 \, \Omega + 100 \, \Omega = 1100 \, \Omega
\]

### Step 3: Calculate Total Current \( I_{\text{TOT}} \)

Using Ohm's Law, the total current \( I_{\text{TOT}} \) is given by:
\[
I_{\text{TOT}} = \frac{U_{\text{TOT}}}{R_{\text{total}}}
\]
Substituting \( U_{\text{TOT}} = 230 \, \text{V} \) and \( R_{\text{total}} = 1100 \, \Omega \):
\[
I_{\text{TOT}} = \frac{230}{1100} \approx 0.209 \, \text{A}
\]

### Step 4: Voltage Across \( R_1 \) (\( U_1 \))

The voltage across \( R_1 \), denoted \( U_1 \), is:
\[
U_1 = I_{\text{TOT}} \times R_1
\]
Substituting \( I_{\text{TOT}} \approx 0.209 \, \text{A} \) and \( R_1 = 1000 \, \Omega \):
\[
U_1 = 0.209 \times 1000 = 209 \, \text{V}
\]

### Step 5: Voltage Across the Parallel Branch (\( U_2 \))

The voltage across the parallel combination of \( R_2 \) and \( R_3 \), denoted \( U_2 \), is the same for both resistors because they are in parallel:
\[
U_2 = U_{\text{TOT}} - U_1
\]
Substituting \( U_{\text{TOT}} = 230 \, \text{V} \) and \( U_1 = 209 \, \text{V} \):
\[
U_2 = 230 - 209 = 21 \, \text{V}
\]

### Step 6: Currents Through \( R_2 \) and \( R_3 \) (\( I_1 \) and \( I_2 \))

Since \( R_2 \) and \( R_3 \) are in parallel, the current through each resistor is given by Ohm's Law.

- For \( I_1 \) through \( R_2 \):
\[
I_1 = \frac{U_2}{R_2} = \frac{21}{200} = 0.105 \, \text{A}
\]

- For \( I_2 \) through \( R_3 \):
\[
I_2 = \frac{U_2}{R_3} = \frac{21}{200} = 0.105 \, \text{A}
\]

Thus, the current through both resistors is the same because \( R_2 = R_3 \).

### Final Results:

- Total current: \( I_{\text{TOT}} \approx 0.209 \, \text{A} \)
- Current through \( R_2 \) (\( I_1 \)): \( I_1 = 0.105 \, \text{A} \)
- Current through \( R_3 \) (\( I_2 \)): \( I_2 = 0.105 \, \text{A} \)
- Voltage across \( R_1 \) (\( U_1 \)): \( U_1 = 209 \, \text{V} \)
- Voltage across the parallel branch (\( U_2 \)): \( U_2 = 21 \, \text{V} \)

Would you like further details or clarifications?

Here are five related questions:
1. How does the total resistance change if \( R_2 \) or \( R_3 \) is altered?
2. What happens to the total current if the total voltage is increased?
3. Can you describe how to solve for power dissipation in each resistor?
4. How does the parallel resistor configuration affect the total circuit behavior?
5. How would the current values change if \( R_1 \) were decreased?

**Tip**: Always start by simplifying parallel and series resistances before applying Ohm's Law.

Beräkna strömmarna I_TOT, I1, och I2, samt spänningarna U1 och U2.

This detailed solution walks through calculating total current I_TOT, branch currents I1 and I2, and voltages U1 and U2 for a circuit consisting of a 1000Ω resistor in series with a parallel combination of two 200Ω resistors, with a 230V power supply. Key concepts include Ohm's Law and series-parallel resistance calculations.

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