If the voltage in a.c. cirucit is represented by the equation.
$V = 220 \sqrt{2} \sin (314 t - ϕ)$
Calculate (a) peak and rms value of the voltage, (b) average voltage, (c) frequency of a.c.

Solution

(a) For a.c. voltage, V = V₀ sin (ωt – ϕ)
The peak voltage value is ,

$V_{0} = 220 \sqrt{2} = 311 V$

The rms value of voltage

$V_{rms} = \frac{V_{0}}{\sqrt{2}} V_{rms} = 220 V$

(b) Average voltage in full cycle is zero.

Average voltage in half cycle is

$V_{av} = \frac{2}{π} V_{0} = \frac{2}{π} \times 311 = 198.17 V$

(c) As,

$ω = 2 πf a n d 2 πf = 314$

i.e., $f = \frac{314}{2 \times π} = 50 Hz$
which, is the required frequency of AC .

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If the voltage in a.c. cirucit is represented by the equation.
$V = 220 \sqrt{2} \sin (314 t - ϕ)$
Calculate (a) peak and rms value of the voltage, (b) average voltage, (c) frequency of a.c.

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If the voltage in a.c. cirucit is represented by the equation.
$V = 220 \sqrt{2} \sin (314 t - ϕ)$
Calculate (a) peak and rms value of the voltage, (b) average voltage, (c) frequency of a.c.