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-1
V - Vc dVc RC dt
-t
K
RC
When, t 0, Vc 0
log V - Vc
(i )
log V K
dq
Vc
dt
d CVc
(ii )
Solve equation (i) and (ii)
-t
log V - Vc
log V
RC
-t
log V - Vc - log V
RC
V - Vc -t
log
V RC
-t
K
RC
When, t 0, Vc V
log Vc
(i )
log V K
(ii )
Solve equation (i ) and (ii )
-t
log Vc
log V
RC
-t
log Vc - log V
RC
Vc -t
log
V RC
Vc
V
-t
RC
e
-t
Vc Ve RC
-t
V - Vc RC
V e
-t
V
1- c e RC
V
PiyushRupala, EE Department
Basic Electrical Engineering (3110005)
25
1
...
C
...
632 V
vc
vc
0
...
46Charging voltage of capacitor
Figure 1
...
37 Im
ic
0
...
47Charging current of capacitor
Figure 1
...
16
...
D
...
Circuits
Charging of Inductor
R
+
Discharging of Inductor
-
+
VR
V
+
-
-
VR
+
L
VL
R
V
+
-
+
L
VL
-
Figure 1
...
50Charging of inductor
From KVL,
di
V - iR - L 0
dt
di
V - iR L
dt
di
dt
V - iR
L
1
1
di dt
V - iR
L
-R
-R
di dt
V - iR
L
-R
log V - iR t K
L
When, t 0, i 0
log V K
-R
log V - iR t log V
L
-R
log V - iR - log V t
L
V - iR -R
log
t
V L
-R
V - iR L t
e
V
-R
t
R
1- i e L
V
-R
t
V
i 1- e L
R
-R
t
i Im 1- e L
(i )
(ii )
Solve equation (i ) and (ii )
i Im 1- e λt
-
From KVL,
di
-iR - L 0
dt
di
-iR L
dt
di
-R
di
i
L
1
-R
di
dt
i
L
-R
log i t K
L
V
When, t 0, i
R
V
log K
R
Solve (i ) and (ii )
(i )
(ii )
-R
V
log i t log
L
R
V -R
log i - log t
R L
i -R
t
log
V L
R
i - R t
e L
V
R
-R
V t
i e L
R
V λt
i e
R
PiyushRupala, EE Department
Basic Electrical Engineering (3110005)
27
1
...
C
...
632 Im
-R
t
i Im 1 - e L
i
iL
iL
V λt
e
R
0
...
52Charging current of inductor
PiyushRupala, EE Department
λ
t
Figure 1