AEE1000 / MEC1151- Electrical Circuits and Analysis
Dr Hong Fan, University of Glasgow, 2022
Tutorial – Topic 5: AC Fundamentals
[Capacitors]
5.1 If the voltage across a 5 F capacitor is 2te−3t find the current and the power.
I / t) cdvlt)
=
at
pct) = vet) ilt)
d - 3ᵗ 3ᵗ 3ᵗ
= 5 ate
3.f) e-
-
.
at = ate .
10 (I -
* 3T d
= 5 ( at Ex C- + e- ax 2T ) = 20T ( I -3T)e
-
Gt
w
ˢᵗ 3ᵗ
= 5 Cat e- . .
-3 + e- . 2)
- 3ᵗ -3T
= 5 I 2@ w Ote )
-3T
= 10 ( I -3T ) @ A
*
5.2 A current of 6sin4t A flows through a 2 F capacitor. Find the voltage v(t) across the capacitor given
that v(0) = 1V.
✓ It ) = { filth
to
+ v1 to )
t
= ÷f 0
65in 4T dt + I
=
¥ [ -
Cocos ut .
IT] ! + I
=
b- ( % -
cos ↳t -
l
-
% cos 410) )) + I
=
-
% cos 4£ t 0.75 + I
75 COS 4T + I -75 V
= -
O -
#
5.3 Determine the equivalent capacitance at terminals a-b of the circuit in Figure 5.1.
Figure 5.1
t
12 )
' -
4µF } 12µF capacitor :( 4
+ = 3nF
3µF // 3µF = 6nF
" " "
( +
b)
0µF } 6µF capacitor : 6 = 3nF
2µF /13µF =
5µF
"
¥)
'
:(
-
5µF } 5µF capacitor
+
5 = 2.5µF
i.
Ceq =
2.5µF
#
1
Dr Hong Fan, University of Glasgow, 2022
Tutorial – Topic 5: AC Fundamentals
[Capacitors]
5.1 If the voltage across a 5 F capacitor is 2te−3t find the current and the power.
I / t) cdvlt)
=
at
pct) = vet) ilt)
d - 3ᵗ 3ᵗ 3ᵗ
= 5 ate
3.f) e-
-
.
at = ate .
10 (I -
* 3T d
= 5 ( at Ex C- + e- ax 2T ) = 20T ( I -3T)e
-
Gt
w
ˢᵗ 3ᵗ
= 5 Cat e- . .
-3 + e- . 2)
- 3ᵗ -3T
= 5 I 2@ w Ote )
-3T
= 10 ( I -3T ) @ A
*
5.2 A current of 6sin4t A flows through a 2 F capacitor. Find the voltage v(t) across the capacitor given
that v(0) = 1V.
✓ It ) = { filth
to
+ v1 to )
t
= ÷f 0
65in 4T dt + I
=
¥ [ -
Cocos ut .
IT] ! + I
=
b- ( % -
cos ↳t -
l
-
% cos 410) )) + I
=
-
% cos 4£ t 0.75 + I
75 COS 4T + I -75 V
= -
O -
#
5.3 Determine the equivalent capacitance at terminals a-b of the circuit in Figure 5.1.
Figure 5.1
t
12 )
' -
4µF } 12µF capacitor :( 4
+ = 3nF
3µF // 3µF = 6nF
" " "
( +
b)
0µF } 6µF capacitor : 6 = 3nF
2µF /13µF =
5µF
"
¥)
'
:(
-
5µF } 5µF capacitor
+
5 = 2.5µF
i.
Ceq =
2.5µF
#
1
