In the circuit in figure, the emf from the battery is equal to 30 V, L= 5H, R1 = 10 ohms and R2 20 ohms. Calculate how much time has to pass after closing the switch K for the current in the resistors to be the same. R, D R1 3.

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**Problem Statement:**

In the circuit shown in the figure, the electromotive force (emf) from the battery is equal to 30 V, the inductance \( L \) is 5 H, \( R_1 \) is 10 ohms, and \( R_2 \) is 20 ohms. Calculate how much time must pass after closing the switch \( K \) for the current in the resistors to be the same.

**Diagram Explanation:**

The provided diagram is a schematic of an electrical circuit. Here are the key components:

1. **Battery (\( \varepsilon \))**: Provides an emf of 30 V.
2. **Inductor (L)**: Has an inductance of 5 H, positioned on the top horizontal branch between points B and C.
3. **Resistors ( \( R_1 \) and \( R_2 \))**: 
   - \( R_1 \) is 10 ohms, located on the top right vertical branch between points C and D.
   - \( R_2 \) is 20 ohms, placed on the bottom horizontal branch between points A and D.
4. **Switch \( K \)**: Placed on the bottom left branch next to the battery, initially open, and is then closed to allow current to flow through the circuit.

**Additional Details:**

- **Points in the Circuit**: 
  - \( A \) is connected to the positive terminal of the battery.
  - \( B \) is connected to the other end of the inductor.
  - \( C \) is connected to the other end of \( R_1 \).
  - \( D \) is a common point connected to \( R_1 \), \( R_2 \), and one end of the inductor.

**Objective:**

Calculate the time required after closing the switch \( K \) for the current flowing through \( R_1 \) and \( R_2 \) to be the same. Use the given values of emf, inductance, and resistances to perform the calculations and derive the time constant of the circuit.
Transcribed Image Text:**Problem Statement:** In the circuit shown in the figure, the electromotive force (emf) from the battery is equal to 30 V, the inductance \( L \) is 5 H, \( R_1 \) is 10 ohms, and \( R_2 \) is 20 ohms. Calculate how much time must pass after closing the switch \( K \) for the current in the resistors to be the same. **Diagram Explanation:** The provided diagram is a schematic of an electrical circuit. Here are the key components: 1. **Battery (\( \varepsilon \))**: Provides an emf of 30 V. 2. **Inductor (L)**: Has an inductance of 5 H, positioned on the top horizontal branch between points B and C. 3. **Resistors ( \( R_1 \) and \( R_2 \))**: - \( R_1 \) is 10 ohms, located on the top right vertical branch between points C and D. - \( R_2 \) is 20 ohms, placed on the bottom horizontal branch between points A and D. 4. **Switch \( K \)**: Placed on the bottom left branch next to the battery, initially open, and is then closed to allow current to flow through the circuit. **Additional Details:** - **Points in the Circuit**: - \( A \) is connected to the positive terminal of the battery. - \( B \) is connected to the other end of the inductor. - \( C \) is connected to the other end of \( R_1 \). - \( D \) is a common point connected to \( R_1 \), \( R_2 \), and one end of the inductor. **Objective:** Calculate the time required after closing the switch \( K \) for the current flowing through \( R_1 \) and \( R_2 \) to be the same. Use the given values of emf, inductance, and resistances to perform the calculations and derive the time constant of the circuit.
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