Question 452: AC fundamentals

Question

An inductor 20 mH, a capacitor 100 $$\mu $$F and
a resistor 50 $$\Omega $$ are connected in series across
a source of emf, V = 10 sin 314 t. The power
loss in the circuit is

Accepted Answer

Average power in impedance
Z = $$\sqrt {{R^2} + {{\left( {{X_C} - {X_L}} ight)}^2}} $$
where X
C
= capacitive
reactance and X
L
= inductive reactance.
Also X
C
= $${1 \over {\omega C}}$$ and X
L
= $$\omega L$$
$$ 	herefore $$ Z = $$\sqrt {{{\left( {50} ight)}^2} + {{\left( {{1 \over {314 	imes 100 	imes {{10}^{ - 6}}}} - 314 	imes 20 	imes {{10}^{ - 3}}} ight)}^2}} $$
$$ \Rightarrow $$ Z = 56.15 $$\Omega $$
I
rms
= $${{{V_{rms}}} \over Z}$$ = $${{{V_m}} \over {\sqrt 2  	imes Z}} = {{10} \over {\sqrt 2  	imes 56}}$$
Hence power loss in the circuit
= $${\left( {{{10} \over {\sqrt 2  	imes 56}}} ight)^2} 	imes 50$$ = 0.79 W

Answer

0.79 W

Answer

0.43 W

Answer

2.74 W

Answer

1.13 W

AC fundamentals

An inductor 20 mH, a capacitor 100 $\mu F and a resistor 50 \Omega $ are connected in series across a source of emf, V = 10 sin 314 t. The power loss in the circuit is

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