Two capacitors C₁ and C₂ are connected as shown in the diagram. The capacitance C₂ is twice C₁ when the key is opened the energy stored up in C₁ is W. If the key is later closed and the system is allowed to attain electrical equilibrium, the total energy stored in the system will be

OsagieN

2 years ago

𝐂₁ 𝐚𝐧𝐝 𝐂₂ 𝐚𝐫𝐞 @ 𝐭𝐡𝐞 𝐬𝐚𝐦𝐞 𝐩𝐨𝐭𝐞𝐧𝐭𝐢𝐚𝐥

𝐄𝐧𝐞𝐫𝐠𝐲 𝐬𝐭𝐨𝐫𝐞𝐝 𝐢𝐧 𝐂₁.....𝐖₁ = ½𝐂₁𝐕²...........𝐢

𝐄𝐧𝐞𝐫𝐠𝐲 𝐬𝐭𝐨𝐫𝐞𝐝 𝐢𝐧 𝐂₂.....𝐖₂ = ½𝐂₂𝐕²...........𝐢𝐢

𝐓𝐫𝐚𝐧𝐬𝐩𝐨𝐬𝐞 𝐞𝐪𝐧 𝐢 𝐚𝐧𝐝 𝐢𝐢 𝐭𝐨 𝐦𝐚𝐤𝐞 𝐯 𝐭𝐡𝐞 𝐬𝐮𝐛𝐣𝐞𝐜𝐭 𝐨𝐟 𝐭𝐡𝐞 𝐟𝐨𝐫𝐦𝐮𝐥𝐚 𝐚𝐧𝐝 𝐞𝐪𝐮𝐚𝐭𝐞 𝐛𝐨𝐭𝐡 𝐞𝐪𝐮𝐚𝐭𝐢𝐨𝐧𝐬.

𝐖₁/𝐂₁ = 𝐖₂/𝐂₂ ...........𝐂₂ = 𝟮𝐂₁

𝐖₁/𝐂₁ = 𝐖₂/𝟮𝐂₁

𝐖₂ = 𝟮𝐖₁...........................𝗶𝗶𝗶

𝐓𝐨𝐭𝐚𝐥 𝐞𝐧𝐞𝐫𝐠𝐲 𝐬𝐭𝐨𝐫𝐞𝐝 = 𝐖₁ + 𝐖₂ = 𝐖₁ + 𝟮𝐖₁ = 𝟯𝐖₁

𝐄

Doctordanny

4 years ago

1
2

C

r
2

=

1
2

(
C
−
1
+

C
2

)

V
2

=
(
3

C
1

)

V
2