Problem 2 Find the phase relationship between the following waveforms: v = 25 cos(wt -60°) V i = 8 cos(wt +35°) mA

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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 \(95^\circ\).
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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