Answer

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**Hint:**Power factor is the product of root mean square values of voltage and current and the cosine of the angle between the voltage and the current. Power factors always depend on the relationship between the phase angle of voltage and current.

**Formula used:**

The formula used for calculating the power factor of pure inductor and pure capacitor is given below

$P = {V_{rms}}\,{I_{rms}}\,\cos \phi $

Here, $P$ is the power factor, ${V_{rms}}$ is the root mean square value of voltage, ${I_{rms}}$ is the root mean square value of current and $\phi $ is the angle between the voltage and the current.

**Complete step by step answer:**

Power factor is the product of root mean square values of voltage and current and the cosine of the angle between the voltage and the current. Now, we know that, in the case of a pure inductor or pure capacitor, the phase angle between the voltage and the current is $90^\circ $. Now, the formula used for calculating the power factor of pure inductor and pure capacitor is given below

$P = {V_{rms}}\,{I_{rms}}\,\cos \phi $

Here, $P$ is the power factor, ${V_{rms}}$ is the root mean square value of voltage, ${I_{rms}}$ is the root mean square value of current and $\phi $ is the angle between the voltage and the current.

$ \Rightarrow \,P = {V_{rms}}\,{I_{rms}}\,\cos 90^\circ $

$ \therefore\,P = 0$

Therefore, the power factor of pure inductor and pure capacitor circuit is zero.

**Hence, option A is the correct answer.**

**Note:**Just remember that the power factor is always taken into when the AC current passes through the LCR combination like LC combination, RC combination, LR combination or LCR combination in series or parallel combination. The value of power factor always comes out to be unity or one.

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