Question

In an AC series circuit, the instantaneous current is zero when voltage is maximum. Connected to the source may be a [more than one option may be correct]
A. pure inductor
B. pure capacitor
C. pure resistor
D. combination of an inductor and a capacitor

Answer 1

Hint: Voltage and current are the sin wave functions so to fully fill the situation that the instantaneous current is zero and the voltage across the circuit is maximum. This is only possible when there is a phase difference between current and voltage is\[\pm \dfrac{\pi }{2}\] . Resistor, inductor and capacitor are passive elements which have the ability to restrict the flow of current. The phase difference between current and voltage in case of inductor and capacitor is $\pm \dfrac{\pi }{2}$.

Complete answer:
In an AC series circuit, passive components which can be connected are resistor, inductor and capacitor.

Resistors: these are the two terminal passive elements which are used to reduce current flow, adjust signal level, divide voltages, etc. In short we can say that resistors are used to perform linear operations they don’t have any sort of storage ability. Resistors obey ohm's law. According to ohm's law voltage is directly proportional to the current flowing in the circuit when all physical conditions like temperature, remains constant. So, here we can conclude that there is now phase difference in voltage and current when the resistor is connected to in an AC series circuit.

Phasor difference for resistor:

 

Phase difference, $\omega =0$

Inductor is a two terminal passive element also named as coil. It has an ability to store energy in a magnetic field when connected to an energy source. Inductors also oppose the flow of current. The ability of an inductor by which they oppose the flow of current is known as reactance (denoted by L). The relationship between voltage drop and current flowing across the circuit is given by:
$e=L\dfrac{di}{dt}$
In an inductor circuit current lags voltage by $\dfrac{\pi }{2}$ or u can say by $90{}^\circ $.

Capacitor is also a two terminal passive element which can store energy. Energy storage capacity of a capacitor is known as capacitance (denoted by C). Relationship between voltage drop and current across the circuit is given by:
$I=C\dfrac{dV}{dt}$
In capacitor circuit voltage lags current by $\dfrac{\pi }{2}$ or u can say by $-90{}^\circ $.

The combination of inductor and capacitor also produce a phase difference of 90$^\circ$.
Thus, we can conclude that except option C all options satisfy the given question.

So, the correct answer is “Option A,B and D”.

Note:
We can also answer this question using the waveform representation of voltage and current in all cases. Understand the question correctly and try to analyze the phase different for all the three types of circuit.