When a pure inductor of inductance ( L ), and a pure capacitor of capacitance ( C ) are connected in parallel to a sinusoidal potential difference ( V ), the potential difference ( V_{{L}} ) across the inductor and ( V_{{C}} ) across the capacitor will be:

Explanation

When a pure inductor and a pure capacitor are connected in parallel to a sinusoidal potential difference ( V ), the potential difference across each element will be different. The potential difference across the inductor (( V_{{L}} )) will lead the current by a phase angle of ( frac{pi}{2} ) (90 degrees), and the potential difference across the capacitor (( V_{{C}} )) will lag behind the current by a phase angle of ( frac{pi}{2} ).Therefore, ( V_{{L}} ) and ( V_{{C}} ) are out of phase, and their magnitudes are determined by the values of ( L ), ( C ), and the frequency of the sinusoidal potential difference.Explanations for Wrong Choices:- (a) Same: Incorrect. The potential differences across the inductor and capacitor in parallel will generally be different due to their phase differences.- (c) ( V_{{L}} ) will be more than ( V_{{C}} ): Incorrect. The magnitudes of ( V_{{L}} ) and ( V_{{C}} ) are determined by the characteristics of the inductor and capacitor and can't be determined solely based on the information provided.- (d) ( V_{{L}} ) will be less than ( V_{{C}} ): Incorrect. Similar to (c), the magnitudes depend on the specific values of ( L ), ( C ), and the frequency.So, the correct answer is (b) Different.