Question

In A.C. voltage source, v = v₀ sin t; having a fixed value for v₀ , but of variable frequency, is connected across a given series LCR circuit. The variation of the current I, flowing in the circuit, with ω, (the angular frequency ofthe source) is as shown. The power consumption, in the circuit, at (angular) frequencies ω₁ and ω₂ , is

(1) 50% of that at (angular)frequency ω₀ and the difference, (ω₂- ω₁), increases with an increase in the Q-factor of the circuit

(2) 50% of that at (angular) frequency ω₀ and the difference, (ω₂- ω₁), decreases with an increase in the Q-factor of the circuit

(3) (nearly) 71% of that at (angular) frequency ω₀ and the difference, (ω₂- ω₁) , decreases with an increase in the ‘Q-factor’ of the circuit

(4) (nearly) 71% of that at (angular) frequency ω₀ and the difference, (ω₂- ω₁) , increases with an increase in the ‘Q-factor’ of the circuit

Answer 1

(2) 50% of that at (angular) frequency ω₀ and the difference, (ω₂- ω₁), decreases with an increase in the Q-factor of the circuit

The current value, for ω₁ and ω₂ , is 1/√2 times the current value at ω₀ . Hence the power consumption (αI²) would become (1/2) or 50% of that at ω₀ .

Further, the more the value of Q, the sharper is the resonance of the circuit. This implies that there is a decrease, in the difference, (ω₂ - ω₁) when the Q-further increases.