Problems
Problems 1
Section 8.3 The Response of a First-Order Circuit to a Constant Input 1
P 8.3-13 1
Solucion 1
Calculando V(0) 2
Para t>0 2
Rth 3
VOC 3
Section 8.3 The Response of a First-Order Circuit to a Constant Input
P 8.3-13
The circuit shown in Figure P 8.3-13 is at steady state when the switch opens at time t = 0. Determine v(t)
for t 0.โ‰ฅ
Figure P 8.3-13
Solucion
๐‘ฃ(๐‘ก)=๐‘‰
๐‘œ๐‘
+[๐‘ฃ(0)โˆ’๐‘‰
๐‘œ๐‘
]๐‘’
โˆ’
๐‘ก
ฯ„
๐‘‰
๐‘œ๐‘
=? ๐‘ฃ(0)=? ฯ„=๐‘…
๐‘กโ„Ž
๐ถ=? ๐‘…
๐‘กโ„Ž
=?
1
Calculando V(0)
๐ฟ๐ถ๐พ
๐‘–1+13=๐‘–2
6โˆ’๐‘ฃ๐ด
30๐‘˜
+
36โˆ’๐‘ฃ๐ด
60๐‘˜
=
๐‘ฃ๐ด
60๐‘˜
)*60k(
6โˆ’๐‘ฃ๐ด
30๐‘˜
+
36โˆ’๐‘ฃ๐ด
60๐‘˜
=
๐‘ฃ๐ด
60๐‘˜
2(6โˆ’๐‘ฃ๐ด)+36โˆ’๐‘ฃ๐ด=๐‘ฃ๐ด
12+36=4๐‘ฃ๐ด
๐‘ฃ๐ด=12๐‘‰
๐‘ฃ(0)=12๐‘‰
Para t>0
2
๐‘…
๐‘กโ„Ž
๐‘…๐‘กโ„Ž=
30๐‘˜*60๐‘˜
30๐‘˜+60๐‘˜
=20 ๐‘˜โ„ฆ
๐‘…๐‘กโ„Ž=20 ๐‘˜โ„ฆ
๐‘‰
๐‘‚๐ถ
๐‘‰
๐‘กโ„Ž
=๐‘‰
60๐‘˜
=
6*60๐‘˜
30๐‘˜+60๐‘˜
=4๐‘‰
๐‘‰
๐‘œ๐‘
=4๐‘‰
ฯ„=๐ถ*๐‘…
๐‘กโ„Ž
=5๐‘ฅ10
โˆ’6
*20๐‘ฅ10
3
=0. 1๐‘  =100๐‘š๐‘ 
1
ฯ„
=10 [
1
๐‘ 
, ๐ป๐‘ง]
3
๐‘ฃ(๐‘ก)=๐‘‰
๐‘œ๐‘
+[๐‘ฃ(0)โˆ’๐‘‰
๐‘œ๐‘
]๐‘’
โˆ’
๐‘ก
ฯ„
๐‘ฃ(๐‘ก)=4+[12โˆ’4]๐‘’
โˆ’10๐‘ก
๐‘ฃ(๐‘ก)=4+8๐‘’
โˆ’10๐‘ก
4