The current in a discharging LR circuit is given by i = i₀e^–t/τ where τ is the time constant of the circuit. Calculate the rms current for the period t = 0 to t = τ.

The peak power consumed by a resistive coil when connected to an AC source is 80W. Find the energy consumed by the coil in 100 seconds which is many times larger than the time period of the source.

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 which can be safely connected to this capacitor.

A capacitor of capacitance 10 μF is connected to an oscillator giving an output voltage ϵ = (10V) sin ωt. Find the peak currents in the circuit for ω = 10 s^–1, 100 s^–1, 500 s^–1, 1000 s^–1.

A coil of inductance 5.0 mH and negligible resistance is connected to the oscillator of the previous problem. Find the peak currents in the circuit for ω= 100 s^–1, 500 s^–1, 1000s^–1.