AC Voltage Applied to a Capacitor: Definition, Derivations, Class 12 Notes & Solutions

The current leads the voltage by 90 degrees (π/2 radians) in a purely capacitive AC circuit. In this case, the current gains the maximum value before the voltage in each cycle. Due to the capacitor responding quickly to the change in voltage, we get to see this phase difference.

Also Check: NCERT Solutions

Mathematical Derivation

Given,

$v\left(t\right)=V_m\sin \left(\omega t\right)\left(\text{AC voltage}\right)$

Current through the capacitor:  

$i\left(t\right)=C\frac{dv\left(t\right)}{dt}=C\cdot \frac{d}{dt}[V_m\sin (\omega t\left)\right]=\omega C{V}_m\cos \left(\omega t\right)$

$i\left(t\right)=\omega C{V}_m\sin (\omega t+\frac{\pi }{2})$

Current leads the voltage by 90 degrees. 

A capacitor has two plates placed at a distance. This gap is filled by dielectric substances. When DC is applied to a capacitor, it gets charged and opposes the flow of charges. This happens due to dielectric materials because they prevent direct electron flow between plates. The energy in the capacitor is stored between the plates as potential energy. 

1. Capacitive Reactance ( $X_C$ )

• Opposition to AC Current: A capacitor resists the flow of AC, and this opposition is known as capacitive reactance. 
• Frequency Dependence: Capacitive reactance is frequency dependent.

2. Inverse Relationship:  

• When the frequency increases, capacitive reactance decreases. 
• When the capacitance increases, capacitive reactance decreases. This means a large capacitor opposes less to AC. 

3. No Real Power Dissipation: 

• No power is consumed in an ideal capacitor. It stores the energy and returns it to the source each cycle.

Important Links:

Below is the summary of the AC voltage applied to a capacitor.

Students can find here the NCERT notes for Class 12 Physics.

Students can find here the link for Class 12 Physics NCERT Solutions. These solutions are helpful in exam preparation.