In an a.c. circuit containing ohmic \( E=E_{0} \sin \omega t \), then \( I=I_{0} \sin (\omega t+...

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In an a.c. circuit containing ohmic \( E=E_{0} \sin \omega t \), then \( I=I_{0} \sin (\omega t+\phi) \) resistance \( R \) only, voltage and current are in the same phase.
If \( E=E_{0} \sin \omega t \), \( \phi=\tan ^{-1} \frac{\left(X_{C}-X_{L}\right)}{R} \).
then \( \quad I=I_{0} \sin \omega t \)
Effective resistance in a.c. circuit \( =R \).
The effective resistance of \( R L C \) circuit is
In an a.c. circuit containing inductance \( (L) \) only, \( Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}} \) alternating current \( I \) lags behind the alternating voltage \( \mathrm{Z} \) is called impedance of the circuit. ( \( E \) ) by a phase angle of \( \pi / 2 \). If \( E=E_{0} \sin \omega t \);
Fig. \( 7.5 \) shows what is called impedance then \( I=I_{0} \sin (\omega t-\pi / 2) \)
Inductive reactance, \( X_{L}=\omega L=2 \pi v L \)
In an a.c. circuit containing a capacitor of - capacitance \( C \), alternating current is ahead of alternating voltage by a phase angle of \( \pi / 2 \).
If \( E=E_{0} \sin \omega t \), then \( I=I_{0} \sin (\omega t+\pi / 2) \) triangle.
Capacitative reactance, \( X_{C}=\frac{1}{\omega C}=\frac{1}{2 \pi v C} \)
In an a.c. circui' containing ohmic resistance \( R \), an inductance \( L \) and a capacitance \( C \) in series if
FIGURE \( 7.5 \)
Which of the following statements are true ?
(i) Through ohmic resistance, altemating voltage and current are in same phase.
(ii) Through an inductor, alt. current lags behind the alt. voltage by \( 90^{\circ} \).
(iii) Through a capacitor, alt. current leads the alt. voltage by \( 90^{\circ} \).
(iv) In RLC circuit, alt. current and voltage are in same phase.
(a) (i) and (ii) only
(b) (i) and (iii) only
(c) (i) and (iv) only
(d) (i), (ii) and (iii) only
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