A coil of inductance L $$=$$ $$5/8$$ H and of $$resistanceR=62.8$$Ωis connected to the mains alternating voltage of frequency $$50Hz$$. What can be the capacitance of the capacitor (in$$ μ$$F) connected in series with the coil if the power dissipated has to remain unchanged? Take π$$2=10$$

Question

A coil of inductance L $$=$$ $$5/8$$ H and of $$resistanceR=62.8$$Ωis connected to the mains alternating voltage of frequency $$50Hz$$. What can be the capacitance of the capacitor (in$$ μ$$F) connected in series with the coil if the power dissipated has to remain unchanged? Take π$$2=10$$

Infinity Learn · Accepted Answer

$$Pav=EvIvcos$$ϕ$$=EvEvZR/ZZ$$ has to be same in both cases.$$Z1=Z2$$⇒$$R2+XL2=R2+(XC-XL)2$$⇒$$XL=XC-XL$$⇒$$2XL=XC$$⇒$$2$$ω$$L=1$$ωC⇒$$C=12$$ω$$2L$$⇒$$C=12$$×$$(2$$$$π$$$$f)2L=12$$×$$4$$$$π$$$$2$$×$$(50)2$$×$$5/8=8$$×$$10-6F$$

AC Circuits

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A coil of inductance L = 5/8 H and of resistance $R = 62.8 Ω$ is connected to the mains alternating voltage of frequency 50Hz. What can be the capacitance of the capacitor (in $μ F$ ) connected in series with the coil if the power dissipated has to remain unchanged? Take $π^{2} = 10$

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AC Circuits

Unlock the full solution & master the concept.

A coil of inductance L = 5/8 H and of resistanceR=62.8Ωis connected to the mains alternating voltage of frequency 50Hz. What can be the capacitance of the capacitor (in μF) connected in series with the coil if the power dissipated has to remain unchanged? Take π2=10

Pav=EvIvcosϕ=EvEvZR/ZZ has to be same in both cases.Z1=Z2⇒R2+XL2=R2+(XC-XL)2⇒XL=XC-XL⇒2XL=XC⇒2ωL=1ωC⇒C=12ω2L⇒C=12×(2πf)2L=12×4π2×(50)2×5/8=8×10-6F

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A coil of inductance L = 5/8 H and of resistance $R = 62.8 Ω$ is connected to the mains alternating voltage of frequency 50Hz. What can be the capacitance of the capacitor (in $μ F$ ) connected in series with the coil if the power dissipated has to remain unchanged? Take $π^{2} = 10$