Calculate the source current i (in mA), if the source voltage (VAB) is 5.73 volt V. AB i1 1 H 12 2 H B L1 L2

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

**Problem Statement:**
"Calculate the source current \( i \) (in mA), if the source voltage (\( V_{AB} \)) is 5.73 volts."

**Circuit Description:**
In the given electrical circuit diagram:

- \( V_{AB} \) represents the source voltage between points A and B, which is given as 5.73 volts.
- The main current flowing from point A to point B is denoted by \( i \).
- There are two inductors in parallel:
  - Inductor \( L1 \) with inductance \( 1 \, H \) (\( H \) stands for henry, the unit for inductance), carrying current \( i1 \).
  - Inductor \( L2 \) with inductance \( 2 \, H \), carrying current \( i2 \).

### Analysis of the Circuit:
To analyze this circuit:

1. **Identify the Configuration:**
   - The two inductors are in parallel between points A and B.

2. **Apply the Source Voltage:**
   - The voltage across each inductor in parallel is the same and equals the source voltage \( V_{AB} = 5.73 \, V \).

3. **Inductors' Response:**
   - Inductors oppose changes in current through them, and the voltage \( V \) across an inductor \( L \) is defined by \( V = L \frac{di}{dt} \).
   - Given that the voltage \( V_{AB} \) is a steady DC value, the time derivative of \( i \) (assuming a steady-state DC) will be zero, and the current through the inductor can be solved based on their steady-state values if applicable.

### Calculation (Steady State DC Analysis):

Given the voltage \( V_{AB} \) is DC and the inductors have reached a steady state:
- The impedance of each inductor in steady state for a DC voltage is zero (short-circuited).
- Hence, current through each inductor can be theoretically very large if ideal (Real inductors have small resistance which can limit current).

### Conclusion:
For educational derivations, typically more context would be needed to solve accurately such as the need to consider initial transient responses or small resistances of inductors in real scenarios. However, in a purely theoretical approach modeling ideal components under specified DC voltage,
Transcribed Image Text:### Circuit Analysis Problem **Problem Statement:** "Calculate the source current \( i \) (in mA), if the source voltage (\( V_{AB} \)) is 5.73 volts." **Circuit Description:** In the given electrical circuit diagram: - \( V_{AB} \) represents the source voltage between points A and B, which is given as 5.73 volts. - The main current flowing from point A to point B is denoted by \( i \). - There are two inductors in parallel: - Inductor \( L1 \) with inductance \( 1 \, H \) (\( H \) stands for henry, the unit for inductance), carrying current \( i1 \). - Inductor \( L2 \) with inductance \( 2 \, H \), carrying current \( i2 \). ### Analysis of the Circuit: To analyze this circuit: 1. **Identify the Configuration:** - The two inductors are in parallel between points A and B. 2. **Apply the Source Voltage:** - The voltage across each inductor in parallel is the same and equals the source voltage \( V_{AB} = 5.73 \, V \). 3. **Inductors' Response:** - Inductors oppose changes in current through them, and the voltage \( V \) across an inductor \( L \) is defined by \( V = L \frac{di}{dt} \). - Given that the voltage \( V_{AB} \) is a steady DC value, the time derivative of \( i \) (assuming a steady-state DC) will be zero, and the current through the inductor can be solved based on their steady-state values if applicable. ### Calculation (Steady State DC Analysis): Given the voltage \( V_{AB} \) is DC and the inductors have reached a steady state: - The impedance of each inductor in steady state for a DC voltage is zero (short-circuited). - Hence, current through each inductor can be theoretically very large if ideal (Real inductors have small resistance which can limit current). ### Conclusion: For educational derivations, typically more context would be needed to solve accurately such as the need to consider initial transient responses or small resistances of inductors in real scenarios. However, in a purely theoretical approach modeling ideal components under specified DC voltage,
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