Question

A coil of resistance 5 Ω and self inductance 0.2 H is connected in series with variable capacitor across a 30 V_(rms), 50 Hz supply. (i) At what capacitance resonance occur? (ii) Find the corresponding current.

Answer 1

Data: R = 5 Ω, L = 0.2 H, e_rms = 30 V, f = 50 Hz

Let C be the capacitance of the capacitor at resonance.

(i) At resonance, `ωL = 1/(ωC)`

∴ Capacitance,

C = `1/(ω^2C) = 1/((2πf)^2 L) = 1/(4π^2f^2L)`

= `1/(4 xx (3.142)^2 xx (50)^2 xx 0.2)`

= 50.65 × 10⁻⁶ F

= 50.65 μF

(ii) At resonance, the current (irms) is maximum and it is given by

`i_(rms) = e_(rms)/R`

= `30/5`

= 6A