What resistance should be added in series with a 7.53-mH inductor to complete an LR circuit with a time constant of 19.5 us?
What resistance should be added in series with a 7.53-mH inductor to complete an LR circuit with a time constant of 19.5 us?
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Question
![**Problem Statement:**
What resistance should be added in series with a 7.53-mH inductor to complete an LR circuit with a time constant of 19.5 µs?
**Solution:**
To solve this problem, we use the formula for the time constant (\(\tau\)) of an LR circuit:
\[
\tau = \frac{L}{R}
\]
Where:
- \(\tau\) is the time constant in seconds,
- \(L\) is the inductance in henrys (H),
- \(R\) is the resistance in ohms (\(\Omega\)).
Given:
- \(L = 7.53 \, \text{mH} = 7.53 \times 10^{-3} \, \text{H}\),
- \(\tau = 19.5 \, \mu\text{s} = 19.5 \times 10^{-6} \, \text{s}\).
Rearranging the formula to solve for resistance:
\[
R = \frac{L}{\tau}
\]
Substitute the given values:
\[
R = \frac{7.53 \times 10^{-3}}{19.5 \times 10^{-6}}
\]
Calculate \(R\) to find the required resistance to achieve the given time constant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F047a7e6a-f025-4b5b-ab83-4ffe14f69253%2F2bcc6e9a-96cd-4995-96ff-759d892318e5%2Fwejdeso_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
What resistance should be added in series with a 7.53-mH inductor to complete an LR circuit with a time constant of 19.5 µs?
**Solution:**
To solve this problem, we use the formula for the time constant (\(\tau\)) of an LR circuit:
\[
\tau = \frac{L}{R}
\]
Where:
- \(\tau\) is the time constant in seconds,
- \(L\) is the inductance in henrys (H),
- \(R\) is the resistance in ohms (\(\Omega\)).
Given:
- \(L = 7.53 \, \text{mH} = 7.53 \times 10^{-3} \, \text{H}\),
- \(\tau = 19.5 \, \mu\text{s} = 19.5 \times 10^{-6} \, \text{s}\).
Rearranging the formula to solve for resistance:
\[
R = \frac{L}{\tau}
\]
Substitute the given values:
\[
R = \frac{7.53 \times 10^{-3}}{19.5 \times 10^{-6}}
\]
Calculate \(R\) to find the required resistance to achieve the given time constant.
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