Q11 of 26 Page 1

A. 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?

B. Without making any other change, find the value of the additional capacitor to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.


Given,


Inductance, L = 100 mH = 100×10-3 H,


Capacitance, C = 2μ F = 2× 10-6 F


Resistance, R = 400 Ω


ω = 1000


(A) For phase difference,



Where, ω = angular speed of cycles


L = inductance


C = Capacitance


R = resistance


Thus,





∴


= 1350


And current is in leading phase since


(B) Unit power factor,



Where,


R = resistance


L = Inductance


C’ = total capacitance


Given, unit power factor, cosϕ = 1


⇒


⇒


∴



= 10 μF


Thus, additional capacitance needed in parallel,


Ca = C’ – C


= 10 μF – 2 μF


= 8 μF


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