Question 229: AC fundamentals

Question

An ideal capacitor of capacitance $$0.2\,\mu F$$ is charged to a potential difference of $$10$$ $$V.$$ The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance $$0.5$$ $$mH.$$ The current at a time when the potential difference across the capacitor is $$5$$ $$V,$$ is :

Accepted Answer

Capacitance, C = 0.2 $$\mu $$F = 0.2 $$ 	imes $$ 10
$$-$$6
F
Inductance, L = 0.5 m H = 0.5  $$ 	imes $$ 10
$$-$$3
H
Let, current = I.
Using energy conservation,
U
E
+ 0 = U
E
'
+ U
b
'
$$ \Rightarrow $$$$\,\,\,\,$$ $${1 \over 2}$$ cv
2
+ 0 = $${1 \over 2}$$ c$$v_1^2$$ + $${1 \over 2}$$LI
2
$$ \Rightarrow $$$$\,\,\,\,$$ $${1 \over 2}$$ $$ 	imes $$ 0.2 $$ 	imes $$  10
$$-$$6
$$ 	imes $$ 10
2
= $${1 \over 2} 	imes $$ 0.2 $$ 	imes $$ 10
$$-$$6
$$ 	imes $$ 5
2
+ $${1 \over 2}$$ $$ 	imes $$ 0.5 $$ 	imes $$ 10
$$-$$3
$$ 	imes $$ I
2
By solving this,
I = $$\sqrt 3  	imes $$ 10
$$-$$1
A
= 0.17 A.

Answer

$$0.34\,\,A$$

Answer

$$0.25\,\,A$$

Answer

$$0.17\,\,A$$

Answer

$$0.15\,\,A$$

AC fundamentals

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