the rms value of alternating current shown in the diagram below is
LectureNotes said the rms value of the alternating current shown in the diagram below is… What is it exactly?
Answer:
Without seeing the exact waveform from the diagram, it’s hard to provide a single numeric answer for the root mean square (rms) value of the alternating current. The rms value depends on the specific shape (sinusoidal, square, triangular, etc.) and amplitude of the waveform. Below are some common waveforms and their corresponding rms values (assuming amplitude = I_m):
- Pure Sinusoidal Wave
- Formula: I_{\mathrm{rms}} = \frac{I_m}{\sqrt{2}}
- Square Wave
- Formula: I_{\mathrm{rms}} = I_m
- Triangular Wave
- Formula: I_{\mathrm{rms}} = \frac{I_m}{\sqrt{3}}
- Half-Wave Rectified Sine
- Formula: I_{\mathrm{rms}} = \frac{I_m}{2}
- Full-Wave Rectified Sine
- Formula: I_{\mathrm{rms}} = \frac{I_m}{\sqrt{2}}
To find the exact rms value, you must:
- Identify the waveform type and amplitude from the diagram.
- Use the appropriate rms formula or integrate the square of the instantaneous current over one complete period:I_{\mathrm{rms}} = \sqrt{\frac{1}{T} \int_{0}^{T} \bigl(i(t)\bigr)^{2} \,dt}.
Below is a summary table of each common waveform and its rms value:
| Waveform Type | Peak Current (Amplitude) | RMS Value |
|---|---|---|
| Sinusoidal | I_m | \displaystyle \frac{I_m}{\sqrt{2}} |
| Square wave | I_m | I_m |
| Triangular wave | I_m | \displaystyle \frac{I_m}{\sqrt{3}} |
| Half-wave rectified | I_m | \displaystyle \frac{I_m}{2} |
| Full-wave rectified | I_m | \displaystyle \frac{I_m}{\sqrt{2}} |
If the waveform in your diagram matches one of these, you can pick the corresponding rms formula. Otherwise, you can apply the integral definition above to calculate it exactly.
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