Question

(i) An a.c. source of emf ε = 200 sin omegat is connected to a resistor of 50 Ω . calculate : 

(1) Average current (`"I"_("avg")`)

(2) Root mean square (rms) value of emf 

(ii) State any two characteristics of resonance in an LCR series circuit. 

Answer 1

(1) Given : 

`ε = 200 sin omegat`

`R = 50 Omega`

`ε_0 = 200`

`ε_(av) = ∫_(omegat = 0)^(2pi) (200 sin omegat  d (omegat))/(2pi)`

= `(200[-cos (omegat)]_(0)^(2pi))/(2pi)`

= `(-200[cos 2pi - cos 0])/(2pi)`

`ε_(a"v") = 0`

`I_(a"v") = ε_(a"v")/50 = 0/50 = 0 A`

(2) RMS value of EMF

`ε_(RMS) = ε_0/sqrt(2)`

 = `200/sqrt(2)`

= `200/1.41 = 141.84 V`

(ii) Two characteristic of resonance in series LCR

(a)At resonance impedance of the current is minimum 

Z = R

(b) The net reactance is zero, so the circuit behaves as purely resistive circuit. At resonance frequency peak current is maximum.