Two capacitors having 6 microfarad and 4 microfarad are connected in series across 120V supply.
a) Find the equivalent capacitance.
b) Find the charge on each capacitor
c)How much work is done by the battery in charging the arrangement.
Answers
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Capacitance of the capacitor = \frac{14}{15}
15
14
microfarad
Given:
Two capacitors of capacitance 4 microfarad and 6 microfarad are connected in parallel
This combination is then connected in series to third capacitor.
The equivalent capacitance of the arrangement is \frac{10}{3}
3
10
microfarad
To find:
Capacitance of the capacitor.
Formula used:
For parallel connection,
\frac{1}{Equavalant \ capacitance}
Equavalant capacitance
1
= \frac{1}{C_1}
C
1
1
+ \frac{1}{C_2}
C
2
1
For series connection,
Equavalant capacitance = C_1 + C_2C
1
+C
2
Explanation:
For parallel connection.
\frac{1}{Equavalant \ capacitance}
Equavalant capacitance
1
= \frac{1}{C_1}
C
1
1
+ \frac{1}{C_2}
C
2
1
\frac{1}{Equavalant \ capacitance}
Equavalant capacitance
1
= \frac{1}{4}
4
1
+ \frac{1}{6}
6
1
Equavalant capacitance = \frac{24}{10}
10
24
= \frac{12}{5}
5
12
microfaranide.
This capacitor is connected with another capacitor with capacitance = C_3C
3
And Equavalant capacitance is \frac{10}{3}
3
10
microfarad
So \frac{12}{5}
5
12
+ C_3C
3
= \frac{10}{3}
3
10
C_3C
3
= \frac{10}{3}
3
10
- \frac{12}{5}
5
12
C_3C
3
= \frac{50-36}{15}
15
50−36
C_3C
3
= \frac{14}{15}
15
14
Capacitance of the capacitor = \frac{14}{15}
15
14
microfarad
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