The circuit shown involves calculating the voltage $U$ using the principle of superposition, as the problem is labeled with "Überlagerungssatz" (Superposition Theorem).

Given Formula:

The voltage $U$ is given as: $U = \frac{R R_1}{2R + R_1 + R_2} (I_{q1} - I_{q2})$

Where:

• $R_1$, $R_2$, and $R$ are resistances,
• $I_{q1}$ and $I_{q2}$ are the currents from the two current sources.

Explanation:

1. Superposition Theorem: The superposition theorem states that in a linear circuit with multiple independent sources, the total response (voltage or current) is the sum of the responses caused by each source acting alone, with all other sources replaced by their internal impedances (short circuit for voltage sources and open circuit for current sources).

2. Analyzing the Circuit:

   • The two current sources $I_{q1}$ and $I_{q2}$ contribute currents in opposite directions.
   • The resistances $R_1$, $R_2$, and $R$ form a network that determines how the currents are distributed.

3. Equivalent Resistance: The equivalent resistance seen by each current source is derived from the configuration of $R_1$, $R_2$, and $R$.

4. Voltage Calculation: The voltage $U$ across the resistance $R$ is calculated based on the contribution of each current source, weighted by the network's resistances.

To Solve:

1. Plug in the values of $R_1$, $R_2$, $R$, $I_{q1}$, and $I_{q2}$ into the given formula.
2. Simplify the expression to find the voltage $U$.

Would you like me to:

• Solve the equation step by step with hypothetical values?
• Provide a deeper explanation of how this formula is derived?
• Offer a numerical example?

Related Questions:

1. What is the superposition theorem, and how is it applied in circuits with both voltage and current sources?
2. How do you calculate the equivalent resistance in parallel and series configurations?
3. Why is the direction of currents $I_{q1}$ and $I_{q2}$ important in this problem?
4. How can this circuit be simplified using Thevenin's or Norton's theorem?
5. What happens to $U$ if one of the current sources $I_{q1}$ or $I_{q2}$ is removed?

Tip:

Always check the direction of current sources and the polarity of voltages when applying the superposition theorem. Misinterpreting these can lead to incorrect results!