Understanding the Phase Relationship in AC Circuits:
In an AC circuit: For a pure inductor, the current \( I \) lags the voltage \( V \) by \( 90^\circ \) (or \(\(\frac{\pi}{2}\) \) radians).
For a pure capacitor, the current \( I \) leads the voltage \( V \) by \( 90^\circ \). For a pure resistor, the current and voltage are in phase, meaning that they reach zero and maximum values simultaneously.
Condition for Instantaneous Current to be Zero When Voltage is Maximum:
The given condition (current is zero when voltage is maximum) implies a \( 90^\circ \) phase difference between the current and voltage.
This situation occurs in:
- A pure inductor, where current lags the voltage by \( 90^\circ \).
- A pure capacitor, where current leads the voltage by \( 90^\circ \).
- A combination of an inductor and capacitor (LC circuit), where the phase difference can also result in current being zero when voltage is maximum.
Conclusion:
Since this phase relationship is possible in a pure inductor, pure capacitor, or an LC combination, the correct answer is Option (4): A, B, and D only.
Draw the plots showing the variation of magnetic flux φ linked with the loop with time t and variation of induced emf E with time t. Mark the relevant values of E, φ and t on the graphs.
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: