Thank you for the clarification. If \( R_2 \) and \( R_3 \) are in series, then the calculation changes as follows:

---

### (a) Berechnen Sie den Gesamtwiderstand \( R_{\text{ges}} \) der Schaltung.

1. **Series Combination of \( R_2 \) and \( R_3 \)**:
   \[
   R_{23} = R_2 + R_3
   \]

2. **Parallel Combination of \( R_{23} \) and \( R_4 \)**:
   \[
   R_{234} = \frac{R_{23} \cdot R_4}{R_{23} + R_4} = \frac{(R_2 + R_3) \cdot R_4}{R_2 + R_3 + R_4}
   \]

3. **Total Resistance \( R_{\text{ges}} \)** (series combination of \( R_1 \) and \( R_{234} \)):
   \[
   R_{\text{ges}} = R_1 + R_{234}
   \]
   Substituting \( R_{234} \), we get:
   \[
   R_{\text{ges}} = R_1 + \frac{(R_2 + R_3) \cdot R_4}{R_2 + R_3 + R_4}
   \]

---

### (b) Wie groß sind der Strom \( I \) und die Spannung \( U_4 \)?

1. **Total Current \( I \)** using Ohm's Law:
   \[
   I = \frac{U_0}{R_{\text{ges}}}
   \]

2. **Voltage \( U_4 \) Across \( R_4 \)**:
   Since \( R_{234} \) (which includes \( R_4 \)) is in series with \( R_1 \), the voltage drop across \( R_{234} \) is:
   \[
   U_{234} = I \cdot R_{234}
   \]
   Thus, the voltage across \( R_4 \) specifically is the same as \( U_{234} \), because \( R_4 \) is part of the parallel combination:
   \[
   U_4 = I \cdot R_4
   \]

---

### (c) Berechnen Sie die Spannung \( U_5 \) in Abhängigkeit vom Gesamtwiderstand \( R_{\text{ges}} \).

The voltage \( U_5 \) across the section with \( R_2 \), \( R_3 \), and \( R_4 \) can be expressed in terms of \( R_{\text{ges}} \) as follows:

1. The voltage \( U_5 \) is simply the voltage drop across \( R_{234} \):
   \[
   U_5 = U_0 - (I \cdot R_1)
   \]
2. Substitute \( I = \frac{U_0}{R_{\text{ges}}} \) into the equation:
   \[
   U_5 = U_0 - \left(\frac{U_0}{R_{\text{ges}}} \cdot R_1\right) = U_0 \left(1 - \frac{R_1

Explore the calculation of total resistance in circuits where resistors R2 and R3 are in series. This page covers key concepts of circuit analysis, including Ohm's Law and series/parallel combinations, with detailed examples suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation