Consider the circuit shown below. The switch S is closed for a very long time so that the inductor I, is constant. Find this initial current. Hint: if the current though an inductor is constant then the inductor can be considered as a piece of wire with no resistance. 4.00 2 8.00 2 10.0 V- 8.00 2 1.00 H
Consider the circuit shown below. The switch S is closed for a very long time so that the inductor I, is constant. Find this initial current. Hint: if the current though an inductor is constant then the inductor can be considered as a piece of wire with no resistance. 4.00 2 8.00 2 10.0 V- 8.00 2 1.00 H
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Transcribed Image Text:### Electrical Circuit Analysis: Inductor Behavior Over Time
**Problem Statement:**
Consider the circuit shown below. The switch \(S\) is closed for a very long time, so that the current through the inductor \(I_0\) is constant. Find this initial current.
**Hint:** If the current through an inductor is constant, then the inductor can be considered as a piece of wire with no resistance.
**Circuit Diagram:**
- A 10.0 V voltage source.
- Three resistors with resistances of 4.00 Ω, 8.00 Ω, and 8.00 Ω, configured in series and parallel arrangements.
- An inductor with an inductance of 1.00 H.
```
4.00 Ω
────
│ │
8.00 Ω N
Voltage Source 10.0 V
│ │
S ────── 8.00 Ω 1.00 H
```
**Steps to Determine Initial Current \((I_0)\):**
1. At steady state (when switch \(S\) has been closed for a very long time), the inductor acts as a short circuit (0 Ω).
2. Calculate the equivalent resistance of the circuit.
3. Use Ohm’s Law \(V = IR\) to find the initial current \(I_0\).
**Questions:**
1. Identify the current \(I_0\) through the inductor when the switch \(S\) is closed for a long duration.
- The current, \(I_0\) = ______ Units __________.
2. At \( t = 0 \) the switch is opened. What is the ratio of the current \(I\) through the inductor 56 ms after the switch was opened to the initial current \(I_0\)?
- The ratio of the currents \( \frac{I}{I_0} \) = ______.
By understanding the inductor’s behavior in a closed circuit over a long time period and immediately after opening the switch, students can grasp the effects of inductance on current and its transient response in electrical circuits.
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