Consider the circuit shown, where = 18.0 V, R₁ = 150 2, R₂ = 15.00, and L = 9.00 H. E a R₁ R₂ inductor S b R₁ i (a) Find the current in the circuit (in A) when the switch has been set to position a for a long time. A ms www R₂ (b) Imagine that the switch is thrown quickly from a to b. Compute the initial voltage (in V) across each resistor and across the indu V V V (c) How much time elapses (in ms) before the voltage across the inductor drops to AV = 18.0 V?

Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Educational Website Content: Analyzing an Electrical Circuit**

---

Consider the circuit shown, where:

- Electromotive force, \( \mathcal{E} = 18.0 \, \text{V} \)
- Resistance \( R_1 = 150 \, \Omega \)
- Resistance \( R_2 = 15.0 \, \Omega \)
- Inductance \( L = 9.00 \, \text{H} \)

**Circuit Diagram Explanation:**

The circuit consists of a battery delivering voltage \( \mathcal{E} \) connected to a switch with positions \( a \) and \( b \). The circuit includes two resistors \( R_1 \) and \( R_2 \), and an inductor \( L \).

1. **Finding the Current in the Circuit:**

   (a) Calculate the current in the circuit (in amperes) when the switch is set to position \( a \) for a long duration.

   *Input field: ___ A*

2. **Voltage Across Resistors and Inductor:**

   (b) Quickly switch from position \( a \) to position \( b \). Determine the initial voltage (in volts) across each component:

   - **Voltage across \( R_1 \):** *Input field: ___ V*
   - **Voltage across \( R_2 \):** *Input field: ___ V*
   - **Voltage across the inductor:** *Input field: ___ V*

3. **Time for Voltage Change in Inductor:**

   (c) Calculate how long (in milliseconds) it takes for the voltage across the inductor to decrease to a change in voltage \( \Delta V_L = 18.0 \, \text{V} \).

   *Input field: ___ ms*

---

Feel free to explore this example to understand how circuits with resistors and inductors operate, especially focusing on voltage changes and time constants.
Transcribed Image Text:**Educational Website Content: Analyzing an Electrical Circuit** --- Consider the circuit shown, where: - Electromotive force, \( \mathcal{E} = 18.0 \, \text{V} \) - Resistance \( R_1 = 150 \, \Omega \) - Resistance \( R_2 = 15.0 \, \Omega \) - Inductance \( L = 9.00 \, \text{H} \) **Circuit Diagram Explanation:** The circuit consists of a battery delivering voltage \( \mathcal{E} \) connected to a switch with positions \( a \) and \( b \). The circuit includes two resistors \( R_1 \) and \( R_2 \), and an inductor \( L \). 1. **Finding the Current in the Circuit:** (a) Calculate the current in the circuit (in amperes) when the switch is set to position \( a \) for a long duration. *Input field: ___ A* 2. **Voltage Across Resistors and Inductor:** (b) Quickly switch from position \( a \) to position \( b \). Determine the initial voltage (in volts) across each component: - **Voltage across \( R_1 \):** *Input field: ___ V* - **Voltage across \( R_2 \):** *Input field: ___ V* - **Voltage across the inductor:** *Input field: ___ V* 3. **Time for Voltage Change in Inductor:** (c) Calculate how long (in milliseconds) it takes for the voltage across the inductor to decrease to a change in voltage \( \Delta V_L = 18.0 \, \text{V} \). *Input field: ___ ms* --- Feel free to explore this example to understand how circuits with resistors and inductors operate, especially focusing on voltage changes and time constants.
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