Problem 2 Find the phase relationship between the following waveforms: v = 25 cos(wt -60°) V i = 8 cos(wt +35°) mA
Problem 2 Find the phase relationship between the following waveforms: v = 25 cos(wt -60°) V i = 8 cos(wt +35°) mA
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![**Problem 2**
Find the phase relationship between the following waveforms:
\[ v = 25 \cos(\omega t - 60^\circ) \, \text{V} \]
\[ i = 8 \cos(\omega t + 35^\circ) \, \text{mA} \]
**Explanation:**
This problem involves two waveforms with the same frequency but different phases.
- The voltage waveform \( v \) has a magnitude of 25 volts and a phase angle of \(-60^\circ\).
- The current waveform \( i \) has a magnitude of 8 milliamperes and a phase angle of \(+35^\circ\).
To find the phase relationship, subtract the phase of the current from the phase of the voltage:
\[ \text{Phase difference} = (-60^\circ) - (+35^\circ) = -95^\circ \]
This means the voltage leads the current by \(95^\circ\) or, equivalently, the current lags the voltage by \(95^\circ\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F547803a6-40ba-407b-9edd-fe79ffc19960%2Fabea218c-90c3-40f3-9262-39945b24375e%2Fcmmoyhs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 2**
Find the phase relationship between the following waveforms:
\[ v = 25 \cos(\omega t - 60^\circ) \, \text{V} \]
\[ i = 8 \cos(\omega t + 35^\circ) \, \text{mA} \]
**Explanation:**
This problem involves two waveforms with the same frequency but different phases.
- The voltage waveform \( v \) has a magnitude of 25 volts and a phase angle of \(-60^\circ\).
- The current waveform \( i \) has a magnitude of 8 milliamperes and a phase angle of \(+35^\circ\).
To find the phase relationship, subtract the phase of the current from the phase of the voltage:
\[ \text{Phase difference} = (-60^\circ) - (+35^\circ) = -95^\circ \]
This means the voltage leads the current by \(95^\circ\) or, equivalently, the current lags the voltage by \(95^\circ\).
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