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AC Circuits — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsAC Circuits3 Marks
Question
An alternating emf is given by $e=220 \sin 314.2 t$ (in volt). Find its
(i) peak value
(ii) rms value
(iii) average value over half cycle
(iv) frequency
(iv) period
(vi) value at $\frac{T}{4}$.
✓

Answer

Data: $e =220 \sin 314.2 t (\text { in volt })_{ t } t =\frac{T}{4}$
(i) Comparing the given equation with $e=e_0 \sin \omega t$, we get, peak value, $e_0=220 V$.
(ii) $e_{ rms }= e _{ o } / \sqrt{2}=155.6 V$
(iii) $e _{ av }$ (over half cycle) $=\frac{2}{\pi} e _0=\frac{2(220)}{3.142}=140 V$
(iv) $\omega=2 \pi f=314.2 \therefore$ The frequency,
$
f =\frac{\omega}{2 \pi}=\frac{314.2}{2(3.142)}=50 Hz
$
(v) The period, $T==\frac{1}{f}=\frac{1}{50}=0.02$ same
(vi) $e=220 \sin \left(\frac{2 \pi}{T} \cdot \frac{T}{4}\right)=220 \sin \frac{\pi}{2}=220 v$

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