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전기전자공학개론

대구가톨릭대학교 전기에너지공학과

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제8장 커패시터

커패시터 동작


커패시턴스


커패시터의 종류




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회로에서의 커패시터


회로에서 커패시터의 충전



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∴ where the initial capacitor voltage( 𝑣𝐶(0+)) = 0

𝑣𝐶 𝑡 =1𝐶� 𝑖 𝑡 𝑑𝑡

𝑖(𝑡) = 𝐶𝑑𝑣𝐶 𝑡𝑑𝑡

∴ 𝑤𝑤𝑤𝑤𝑤 𝜏 = 𝑅𝐶

𝐸𝑅𝐶

▣ 축전기의 충전(Charging a Capacitor)

처음에 축전기가 충전되지 않은 상태라고 가정하자.

0=−− IRCq

E

RCq

Rdtdq

−=E

RCCq

RCq

RCC

dtdq EE −

−=−=

dtRCCq

dq 1−=

− E

dtdqI = 이므로


) 0( 전류에서의== tR

Iwhere iE

)(최대전하ECQwhere =

∫∫ −=−

tqdt

RCCqdq

00

1)( E RC

tCCqn −=

−−

EE1

)1()1()( // RCtRCt eQeCtq −− −=−= E

RCti

RCt eIeR

tI //)( −− ==E

RC=τ

시간 상수(time constant): 전류가 처음 값의 1/e로 감소하는 데 걸리는 시간




𝑣𝑅 𝑡 +𝑣𝐶 𝑡 = 0 → 𝑅𝑖 𝑡 +𝑣𝐶 𝑡 = 0

𝑅𝐶𝑣𝐶 𝑡𝑑𝑡

+𝑣𝐶 𝑡 = 0 →𝑣𝐶 𝑡𝑑𝑡

+1𝑅𝐶

𝑣𝐶 𝑡 = 0

𝑅𝐶 𝑠𝑉𝑐 𝑠 − 𝑣𝑐 0+ + 𝑉𝑐 𝑠 = 0 → 𝑉𝑐 𝑠 (𝑅𝐶𝑠 + 1) = 0

𝑉𝑐 𝑠 =𝑅𝐶𝑣𝑐 0+𝑅𝐶𝑠 + 1

=𝑣𝑐 0+𝑠 + 1 𝑅𝐶⁄ ∴ 𝑤𝑤𝑤𝑤𝑤 𝑣𝑐 0+ = E

∴ 𝑣𝑐 𝑡 = E ∙ 𝑤−1𝑅𝐶𝑡 𝑉 ∴ 𝑤𝑤𝑤𝑤𝑤 𝜏 = 𝑅𝐶

∴ 𝑖 𝑡 = 𝐶

𝑣𝐶 𝑡𝑑𝑡

= −𝐸𝑅𝐶

∙ 𝑤−1𝑅𝐶𝑡 [𝐴]

▣ 축전기의 방전(Discharging a Capacitor)

처음에 축전기가 전하 Q로 완전히 충전된 상태에서 스위치를 b로 닫는다고 가정하자.

0=−− IRCq

Cq

dtdqR =− dt

RCqdq 1

−=

RCt

Qqn

dtRCq

dq tq

Q

−=

−= ∫∫

1

10

RCtQetq /)( −=

RCti

RCt eIeRC

QtI //)( −− =−=


커패시터 손상


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