Question

Using phasor diagram for a series LCR circuit connected to an ac source of voltage v = v₀sinωτ, derive the relation for the current flowing in the circuit and the phase angle between the voltage across the resistor and the net voltage in the circuit. 

Draw a plot showing the variation of the current I as a function of angular frequency ‘ω’ of the applied ac source for the two cases of a series combination of (i) inductance L₁ , capacitance C₁  and resistance R₁  and (ii) inductance L₂ , capacitance C₂  and resistance R₂  where R₂  > R₁. 

Write the relation between L₁ , C₁  and L₂ ,C₂  at resonance. Which one, of the two, would be better suited for fine tuning in a receiver set? Give reason

Answer 1

(a) For I_eff flow of current through each element R, L and C, Effective voltage across the combination can be given as.

 

Phase angle between V_R and V_eff is

Variation of the current I as a function of angular frequency ω.
At resonance, when maximum current flows through the circuit.

For fine tuning in the receiver set, combination L₁C₁ and R₁ is better because maximum current flows through the circuit.

From Lenz’s law, induced emf