two capacitance c1 and c2 are combined in series if c1 =10.1 +0.1 and c2 = 5.0+0.2 calculate the combined capacitor
Answers
Answer:
Two capacitors of unknown capacitances C
1
and C
2
are connected first in series and then in parallel across a battery of 100 V. If the energy stored in the two combinations is 0.045 J and 0.25 J respectively, determine the value of C
1
and C
2
. Also calculate the charge on each capacitor in parallel combination
Explanation:
When the two capacitors are in series, the equivalent capacitance, C
s
=
C
1
+C
2
C
1
C
2
When the two capacitors are in parallel, the equivalent capacitance, C
p
=C
1
+C
2
Here, U
s
=
2
1
C
s
V
2
or 0.045=0.5×
C
1
+C
2
C
1
C
2
(100)
2
or 9(C
1
+C
2
)=10
6
C
1
C
2
...(1)
Now, U
p
=
2
1
C
p
V
2
or 0.25=0.5×(C
1
+C
2
)(100)
2
or 0.02(C
1
+C
2
)×10
6
=1...(2)
(1)/(2)⇒450=10
12
C
1
C
2
...(3)
using, (2) ,(3), 0.02(C
1
+
C
1
450×10
−12
)×10
6
=1
Solving, C
1
=25+5
7
μF
C
2
=25−5
7
μF
In parallel, voltage across the capacitors is equal to the supply voltage (100 V).
Q
1
=CV=(2.5+.5
7
)mC
Q
2
=CV=(2.5−.5
7
)mC