de conditions, 8. Under steady - state find i and v in the circuit shown 2 mH +

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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**Problem Statement:**

Under steady-state DC conditions, find \( i \) and \( V \) in the circuit shown.

**Circuit Description:**

- The circuit includes a 10V DC voltage source.
- A 2 kΩ resistor is connected in series with a 2 mH inductor.
- A parallel branch follows, containing a 4 kΩ resistor and a series connection of a 1 kΩ resistor and a 2 μF capacitor.
- The voltage across the capacitor is labeled as \( V \).

**Key Points for Solution:**

1. In steady-state DC conditions, the inductor behaves as a short circuit, and the capacitor behaves as an open circuit.
2. Calculate the current \( i \) flowing through the 2 kΩ and 1 kΩ resistors using Ohm's Law and Kirchhoff's laws.
3. Determine the voltage \( V \) across the open-circuit capacitor.

**Calculations:**

- Determine equivalent resistances.
- Apply Kirchhoff’s voltage and current laws as needed to find \( i \) and \( V \).

This type of analysis helps in understanding DC steady-state behavior of inductors and capacitors and their implications in complex circuits.
Transcribed Image Text:**Problem Statement:** Under steady-state DC conditions, find \( i \) and \( V \) in the circuit shown. **Circuit Description:** - The circuit includes a 10V DC voltage source. - A 2 kΩ resistor is connected in series with a 2 mH inductor. - A parallel branch follows, containing a 4 kΩ resistor and a series connection of a 1 kΩ resistor and a 2 μF capacitor. - The voltage across the capacitor is labeled as \( V \). **Key Points for Solution:** 1. In steady-state DC conditions, the inductor behaves as a short circuit, and the capacitor behaves as an open circuit. 2. Calculate the current \( i \) flowing through the 2 kΩ and 1 kΩ resistors using Ohm's Law and Kirchhoff's laws. 3. Determine the voltage \( V \) across the open-circuit capacitor. **Calculations:** - Determine equivalent resistances. - Apply Kirchhoff’s voltage and current laws as needed to find \( i \) and \( V \). This type of analysis helps in understanding DC steady-state behavior of inductors and capacitors and their implications in complex circuits.
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