AC Voltage Applied to a Capacitor

An a.c. source generating a voltage ε = ε₀ sin ωt is connected to a capacitor of capacitance C. Find the expression for the current I flowing through it. Plot a graph of ε and I versus ωt to show that the current is ahead of the voltage by π/2.

The dielectric strength of air is 3.0 × 10⁶ V/m. A parallel-plate air-capacitor has area 20 cm² and plate separation 0.10 mm. Find the maximum rms voltage of an AC source that can be safely connected to this capacitor.

A bulb rated 60 W at 220 V is connected across a household supply of alternating voltage of 220 V. Calculate the maximum instantaneous current through the filament.

A current i₁ = i₀ sin ωt passes through a resistor of resistance R. How much thermal energy is produced in one time period? A current i₂ = −i₀ sin ωt passes through the resistor. How much thermal energy is produced in one time period? If i₁ and i₂ both pass through the resistor simultaneously, how much thermal energy is produced? Is the principle of superposition obeyed in this case?

An AC source is rated 220 V, 50 Hz. The average voltage is calculated in a time interval of 0.01 s. It

A transformer has 50 turns in the primary and 100 in the secondary. If the primary is connected to a 220 V DC supply, what will be the voltage across the secondary?

Compare resistance and reactance.

A 2 µF capacitor, 100 Ω resistor and 8 H inductor are connected in series with an AC source.
(i) What should be the frequency of the source such that current drawn in the circuit is maximum? What is this frequency called?
(ii) If the peak value of e.m.f. of the source is 200 V, find the maximum current.
(iii) Draw a graph showing variation of amplitude of circuit current with changing frequency of applied voltage in a series LRC circuit for two different values of resistance R₁ and R₂ (R₁ > R₂).
(iv) Define the term 'Sharpness of Resonance'. Under what condition, does a circuit become more selective?