Question:

In an A.C.circuit containing only capacitance, the current

Updated On: Mar 6, 2024
  • leads the voltage by $180^{\circ}$
  • lags the voltage by $90^{\circ}$
  • leads the voltage by $90^{\circ}$
  • remains in phase with the voltage
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The Correct Option is C

Solution and Explanation

In a purely capacitive circuit, where there is no resistance, the current i flowing through it deposits a charge dq on the capacitor in time that is $dq = idt $ $\Rightarrow i=\frac{dq}{dt}$
Now using Kirchoff's law, if total charge deposited on the capacitor is $q$ then $\frac{q}{C}=E_{0} \sin \omega t $ $\Rightarrow q=C E_{0} \sin \omega t $ $\Rightarrow i=\frac{d q}{d t}=C E_{0} \omega \cos \omega t=i_{0} \cos \omega t$ where $i_{0}=\frac{E_{0}}{\left(1 / C_{\omega}\right)}$ = peak current $\therefore i=i_{0} \cos \omega t=i_{0} \sin \left(\omega+\frac{\pi}{2}\right) t$ and $E=E_{0} \sin \omega t$ Hence current is leading the voltage in phase by $\frac{\pi}{2}$
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Concepts Used:

Alternating Current

An alternating current can be defined as a current that changes its magnitude and polarity at regular intervals of time. It can also be defined as an electrical current that repeatedly changes or reverses its direction opposite to that of Direct Current or DC which always flows in a single direction as shown below.

Alternating Current Production

Alternating current can be produced or generated by using devices that are known as alternators. However, alternating current can also be produced by different methods where many circuits are used. One of the most common or simple ways of generating AC is by using a basic single coil AC generator which consists of two-pole magnets and a single loop of wire having a rectangular shape.

Application of Alternating Current

AC is the form of current that are mostly used in different appliances. Some of the examples of alternating current include audio signal, radio signal, etc. An alternating current has a wide advantage over DC as AC is able to transmit power over large distances without great loss of energy.