Question 153: AC fundamentals

Question

A series AC circuit containing an inductor (20 mH), a capacitor (120 $\mu $F) and a resistor (60 $\Omega $) is driven by an AC source of 24V/50 Hz. The energy dissipated in the circuit in 60 s is :

Accepted Answer

Energy dissipated in 60 Sec
= (P
avg
) $ 	imes $ 60
= V
rms
$ 	imes $ I
rms
$ 	imes $ cos$\phi $ $ 	imes $ 60
= V
rms
$ 	imes $ ${{{V_{rms}}} \over Z} 	imes $ cos$\phi $ $ 	imes $ 60
X
L
= $\omega $L = 2$\pi $FL
= 2$\pi $(50)$ 	imes $ 20 $ 	imes $ 10
$-$3
= 2$\pi $ $\Omega $
X
C
= ${1 \over {\omega C}}$
= ${1 \over {2\pi fC}}$
= ${1 \over {2\pi \left( {50} ight) 	imes 120 	imes {{10}^{ - 6}}}}$
= 26.52 $\Omega $
$ 	herefore $   X
C
$-$ X
L
= 20.24 $ \simeq $ 20
$ 	herefore $   Z = $\sqrt {{{\left( {{X_C} - {X_L}} ight)}^2} + {R^2}} $
= $\sqrt {{{\left( {20} ight)}^2} + {{60}^2}} $
= 20  $\sqrt {10} $ $\Omega $
Also cos$\phi $ = ${R \over Z}$ = ${{60} \over {20\sqrt {10} }} = {3 \over {\sqrt {10} }}$
$ 	herefore $   Energy dissipated in 60 sec
= ${{{{\left( {24} ight)}^2}} \over {20\sqrt {10} }} 	imes {3 \over {\sqrt {10} }} 	imes 60$
= 5.17 $ 	imes $ 10
2
J

Answer

5.65 $ 	imes $ 10
2
J

Answer

2.26 $ 	imes $ 10
3
J

Answer

5.17 $ 	imes $ 10
2
J

Answer

3.39 $ 	imes $ 10
3
J

AC fundamentals

A series AC circuit containing an inductor (20 mH), a capacitor (120 \mu F) and a resistor (60 \Omega ) is driven by an AC source of 24V/50 Hz. The energy dissipated in the circuit in 60 s is :

Choose the correct answer: