If the time constant of the LR circuit illustrated below is T-5s, what is L, the unknown inductance? 2H mmm A. 2H B. 7H C. 18H D. 19H E. 20H 2H m ww mu 1.5 зл A
If the time constant of the LR circuit illustrated below is T-5s, what is L, the unknown inductance? 2H mmm A. 2H B. 7H C. 18H D. 19H E. 20H 2H m ww mu 1.5 зл A
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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![### Understanding the LR Circuit
#### Problem Statement:
If the time constant of the LR circuit illustrated below is τ = 5s, what is L, the unknown inductance?
#### Circuit Diagram:
The figure shows an electrical circuit consisting of:
- An inductor of unknown inductance \( L \)
- A series combination of a \( 1 \Omega \) resistor
- A \( 3 \Omega \) resistor
- A parallel combination of two \( 2H \) inductors
The circuit follows this arrangement:
- The unknown inductor \( L \) is in series with the entire branch.
- The two 2H inductors are in parallel with each other.
#### Options:
A. 2H
B. 7H
C. 18H
D. 19H
E. 20H
### Steps to Solve:
1. **Identify the equivalent inductance of the inductors in parallel:**
\[
L_{\text{parallel}} = \left( \frac{1}{2H} + \frac{1}{2H} \right)^{-1} = 1H
\]
2. **Combine the inductors in series:**
Since \( L_{\text{parallel}} \) is in series with \( L \), the total inductance \( L_{\text{total}} \) is:
\[
L_{\text{total}} = L + 1H
\]
3. **Calculate the total resistance in the circuit:**
The resistors are in series:
\[
R_{\text{total}} = 1\Omega + 3\Omega = 4\Omega
\]
4. **Use the formula for the time constant \(\tau\):**
\[
\tau = \frac{L_{\text{total}}}{R_{\text{total}}}
\]
Given \(\tau = 5s \):
\[
5 = \frac{L + 1H}{4\Omega}
\]
5. **Solve for the unknown inductance \( L \):**
\[
L + 1H = 20H
\]
\[
L = 19H
\]
Therefore, the unknown inductance \( L \) is:
#### Answer: D. 19H](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a5ac3c6-e4ab-423a-91e1-ff33bdae0d07%2Ffacdf085-73e6-4c32-8fb0-6f64bc7b6587%2Frvwvssc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the LR Circuit
#### Problem Statement:
If the time constant of the LR circuit illustrated below is τ = 5s, what is L, the unknown inductance?
#### Circuit Diagram:
The figure shows an electrical circuit consisting of:
- An inductor of unknown inductance \( L \)
- A series combination of a \( 1 \Omega \) resistor
- A \( 3 \Omega \) resistor
- A parallel combination of two \( 2H \) inductors
The circuit follows this arrangement:
- The unknown inductor \( L \) is in series with the entire branch.
- The two 2H inductors are in parallel with each other.
#### Options:
A. 2H
B. 7H
C. 18H
D. 19H
E. 20H
### Steps to Solve:
1. **Identify the equivalent inductance of the inductors in parallel:**
\[
L_{\text{parallel}} = \left( \frac{1}{2H} + \frac{1}{2H} \right)^{-1} = 1H
\]
2. **Combine the inductors in series:**
Since \( L_{\text{parallel}} \) is in series with \( L \), the total inductance \( L_{\text{total}} \) is:
\[
L_{\text{total}} = L + 1H
\]
3. **Calculate the total resistance in the circuit:**
The resistors are in series:
\[
R_{\text{total}} = 1\Omega + 3\Omega = 4\Omega
\]
4. **Use the formula for the time constant \(\tau\):**
\[
\tau = \frac{L_{\text{total}}}{R_{\text{total}}}
\]
Given \(\tau = 5s \):
\[
5 = \frac{L + 1H}{4\Omega}
\]
5. **Solve for the unknown inductance \( L \):**
\[
L + 1H = 20H
\]
\[
L = 19H
\]
Therefore, the unknown inductance \( L \) is:
#### Answer: D. 19H
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