Question 471: AC fundamentals

Question

An inductor 20 mH, a capacitor 50 $$\mu F$$ and a resistor 40 $$\Omega $$ are connected in series across a source of emf V = 10 sin 340t. The power loss in A.C. circuit is

Accepted Answer

X
L
= $$\omega $$L = 340 $$ 	imes $$ 20 $$ 	imes $$ 10
-3
= 6.8 $$\Omega $$
X
C
= $${1 \over {340 	imes 50 	imes {{10}^{ - 6}}}}$$ = 58.82 $$\Omega $$
Average power in impedance
Z = $$\sqrt {{R^2} + {{\left( {{X_C} - {X_L}} ight)}^2}} $$
= $$\sqrt {{{40}^2} + {{\left( {58.82 - 6.8} ight)}^2}} $$ = 65.62 $$\Omega $$
Power loss in A.C. circuit,
= V
rms
I
rms
cos$$\phi $$
= $${1 \over 2}$$V
0
I
0
cos$$\phi $$
= $${1 \over 2} 	imes 10 	imes {{10} \over {65.62}} 	imes {{40} \over {65.62}}$$
= 0.46 W

Answer

0.76 W

Answer

0.89 W

Answer

0.51 W

Answer

0.67 W

AC fundamentals

An inductor 20 mH, a capacitor 50 $\mu F and a resistor 40 \Omega $ are connected in series across a source of emf V = 10 sin 340t. The power loss in A.C. circuit is

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