Q13Basic Electrical Engineering

Question

An alternating voltage is given by V=230sin 314t. Calculate frequency and maximum average & RMS value of voltage.

Answer 1

The fundamental equation for an alternating voltage is $v (t) = V_{m} sin (ω t)$ . Comparing this to the given equation $V = 230 sin (314 t)$ :

1. Maximum Value ( $V_{m}$ ): The peak amplitude is directly the coefficient of the sine function. Thus, $V_{m} = 230 Volts$ .
2. Frequency ( $f$ ): The angular velocity $ω = 314 rad/sec$ . Since $ω = 2 π f$ , we have $f = \frac{314}{2 π} = \frac{314}{2 \times 3.1415} \approx 50 Hz$ .
3. RMS Value ( $V_{r m s}$ ): For a pure sine wave, the Root Mean Square value is $0.707$ times the maximum. $V_{r m s} = \frac{V _{m}}{2} = \frac{230}{1.414} = 162.63 Volts$ .
4. Average Value ( $V_{a v g}$ ): The average value over a half cycle is $0.637$ times the maximum. $V_{a v g} = \frac{2 V _{m}}{π} = \frac{460}{3.1415} = 146.42 Volts$ .

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