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Consider the Circuit shown 10mA How much To t=o energy 2kn 8.2 kn 2 kn + V₂ ell İL 10 mH 20 mH Find an expression for in and V₁ if the switch is closed at t = os. is stored in each inductor ? LINO 200

Consider the Circuit shown 10mA How much To t=o energy 2kn 8.2 kn 2 kn + V₂ ell İL 10 mH 20 mH Find an expression for in and V₁ if the switch is closed at t = os. is stored in each inductor ? LINO 200

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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**Problem Description:** Consider the circuit shown in the diagram. **Circuit Details:** - A 10 mA current source is connected in series with a 2 kΩ resistor and a parallel combination of another 2 kΩ resistor and an 8.2 kΩ resistor. - A switch is placed in the circuit at \( t = 0 \). - After the switch, there is a series connection to a 2 kΩ resistor. - This leads to two inductors, one is 10 mH and the other is 20 mH, connected in series with each other. - The current through the inductors is labeled \( i_L \) and the voltage across them is labeled \( V_L \). **Tasks:** 1. Find an expression for \( i_L \) and \( V_L \) if the switch is closed at \( t = 0 \). 2. Calculate how much energy is stored in each inductor. **Solution Approach:** To solve these questions, apply the following steps: - Analyze the circuit initially for \( t < 0 \) and for \( t \geq 0 \) when the switch is closed. - Use Kirchhoff's laws and the properties of inductors to form differential equations as needed. - For energy stored in the inductors, use the formula: \[ \text{Energy} = \frac{1}{2} L i^2 \] where \( L \) is the inductance and \( i \) is the current through the inductor at the steady state. This approach will help derive the expressions for \( i_L \) and \( V_L \), and calculate the energy for each inductor individually.
Transcribed Image Text:**Problem Description:** Consider the circuit shown in the diagram. **Circuit Details:** - A 10 mA current source is connected in series with a 2 kΩ resistor and a parallel combination of another 2 kΩ resistor and an 8.2 kΩ resistor. - A switch is placed in the circuit at \( t = 0 \). - After the switch, there is a series connection to a 2 kΩ resistor. - This leads to two inductors, one is 10 mH and the other is 20 mH, connected in series with each other. - The current through the inductors is labeled \( i_L \) and the voltage across them is labeled \( V_L \). **Tasks:** 1. Find an expression for \( i_L \) and \( V_L \) if the switch is closed at \( t = 0 \). 2. Calculate how much energy is stored in each inductor. **Solution Approach:** To solve these questions, apply the following steps: - Analyze the circuit initially for \( t < 0 \) and for \( t \geq 0 \) when the switch is closed. - Use Kirchhoff's laws and the properties of inductors to form differential equations as needed. - For energy stored in the inductors, use the formula: \[ \text{Energy} = \frac{1}{2} L i^2 \] where \( L \) is the inductance and \( i \) is the current through the inductor at the steady state. This approach will help derive the expressions for \( i_L \) and \( V_L \), and calculate the energy for each inductor individually.
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