Advertisements
Advertisements
Question
(i) Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase : current or voltage ?
(ii) Without making any other change, find the value of the additional capacitor C1, to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.
Solution
(i) Given V = V0sin(1000t + ϕ)
ω = 1000 s-1
Given,
L = 100 mH
C = 2 μF
R = 400 Ω
Phase difference ϕ= tan-1((XL−XC)/R)
XL = ωL = 1000 × 100 × 10-3 = 100 Ω
`X_C=1/(omegaC)=1/(1000xx2xx10^-6)=500Omega`
`ϕ= tan^-1((100−500)/400)= tan^-1(-1)`
ϕ = -450 and the current is leading the voltage.
(ii)
For power factor to be unity, R = Z
or XL = XC
`ω^2 =1/(LC)` (C = resultant capacitance)
`10^6 = 1/(100xx10^-3xxC')`
⇒C' = 10-5 F
For two capacitance in parallel, resultant capacitance C'= C + C1
10-5 = 0.2 x 10-5 + C1
⇒C1 = 8 μF
APPEARS IN
RELATED QUESTIONS
In a series LCR circuit, VL = VC ≠ VR. What is the value of power factor?
A source of ac voltage v = v0 sin ωt, is connected across a pure inductor of inductance L. Derive the expressions for the instantaneous current in the circuit. Show that average power dissipated in the circuit is zero.
Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 µF, and R = 7.4 Ω. It is desired to improve the sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2. Suggest a suitable way.
For a series LCR-circuit, the power loss at resonance is ______.
In series LCR AC-circuit, the phase angle between current and voltage is
A series LCR circuit containing 5.0 H inductor, 80 µF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be ______.
Which of the following combinations should be selected for better tuning of an LCR circuit used for communication?
A series LCR circuit containing a resistance of 120 Ω has angular resonance frequency 4 × 105 rad s-1. At resonance the voltage across resistance and inductance are 60 V and 40 V respectively. At what frequency the current in the circuit lags the voltage by 45°. Give answer in ______ × 105 rad s-1.
Draw the phasor diagram for a series LRC circuit connected to an AC source.
Draw the impedance triangle for a series LCR AC circuit and write the expressions for the impedance and the phase difference between the emf and the current.
