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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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### 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.
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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