Question

A voltmeter connected across a 60Hz ac source reads 240V. Write down the expression of the instanteneous voltage as a function of time.

Answer 1

Answer on Question #45719 – Physics, Electric Circuits

A voltmeter connected across a 60Hz ac source reads 240V. Write down the expression of the instantaneous voltage as a function of time.

AC voltage could be expressed by sinusoidal wave equation:

$$V = V_{peak} \sin(2\pi\nu t)$$

Where $V_{peak}$ – is an amplitude value of a voltage, $\nu$ – is voltage frequency.

For the AC voltmeter will show RMS voltage:

$$V_{rms} = \frac{V_{peak}}{\sqrt{2}}$$

Thus,

$$V_{peak} = V_{rms} \sqrt{2} = 240V \cdot \sqrt{2} \approx 339.4V$$

So, expression of the instantaneous voltage as a function of time:

$$V = 339.4 \sin(2 \cdot 3.14 \cdot 60\,Hz \cdot t)$$ $$V = 339.4 \sin(377t)$$

Answer: instantaneous voltage as a function of time:

$$V = 339.4 \sin(377t)$$

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