Answer:
![Q=1.575*10^-6*9=1.42*10^-5C\\\\U_{c} =\frac{1}{2}*9^{2} *1.575*10^-6=6.38*10^-5J](https://tex.z-dn.net/?f=Q%3D1.575%2A10%5E-6%2A9%3D1.42%2A10%5E-5C%5C%5C%5C%5CU_%7Bc%7D%20%3D%5Cfrac%7B1%7D%7B2%7D%2A9%5E%7B2%7D%20%2A1.575%2A10%5E-6%3D6.38%2A10%5E-5J)
![Q=9.4*10^-6*9=8.46*10^-5C\\\\U_{c} =\frac{1}{2}*9^{2} *9.4*10^-6=3.81*10^-4J](https://tex.z-dn.net/?f=Q%3D9.4%2A10%5E-6%2A9%3D8.46%2A10%5E-5C%5C%5C%5C%5CU_%7Bc%7D%20%3D%5Cfrac%7B1%7D%7B2%7D%2A9%5E%7B2%7D%20%2A9.4%2A10%5E-6%3D3.81%2A10%5E-4J)
Explanation:
<u>a)</u>
<u>Identify the unknown: </u>
The charge and energy stored if the capacitors are connected in series
<u>List the Knowns: </u>
Capacitance of the first capacitor:
= 2цF = 2 x 10-6 F
Capacitance of the second capacitor
= 7.4цF = 7.4 x 10-6 F
Voltage of battery: V = 9 V
<u>Set Up the Problem:
</u>
Capacitance of a series combination:
+............
![\frac{1}{C_{s} } =\frac{1}{2} +\frac{1}{ 7.4} \\C_{s} =\frac{2*7.4}{2+7.4}=1.575 *10^-6 F\\](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7BC_%7Bs%7D%20%7D%20%3D%5Cfrac%7B1%7D%7B2%7D%20%2B%5Cfrac%7B1%7D%7B%207.4%7D%20%5C%5CC_%7Bs%7D%20%3D%5Cfrac%7B2%2A7.4%7D%7B2%2B7.4%7D%3D1.575%20%2A10%5E-6%20F%5C%5C)
Capacitance of a series combination is given by:
![C_{s}=\frac{Q}{V}](https://tex.z-dn.net/?f=C_%7Bs%7D%3D%5Cfrac%7BQ%7D%7BV%7D)
Then the charge stored in the series combination is:
![Q=C_{s} V](https://tex.z-dn.net/?f=Q%3DC_%7Bs%7D%20V)
Energy stored in the series combination is:
![U_{c}=\frac{1}{2} V^{2} C_{s}](https://tex.z-dn.net/?f=U_%7Bc%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%20V%5E%7B2%7D%20C_%7Bs%7D)
<u>Solve the Problem: </u>
![Q=1.575*10^-6*9=1.42*10^-5C\\\\U_{c} =\frac{1}{2}*9^{2} *1.575*10^-6=6.38*10^-5J](https://tex.z-dn.net/?f=Q%3D1.575%2A10%5E-6%2A9%3D1.42%2A10%5E-5C%5C%5C%5C%5CU_%7Bc%7D%20%3D%5Cfrac%7B1%7D%7B2%7D%2A9%5E%7B2%7D%20%2A1.575%2A10%5E-6%3D6.38%2A10%5E-5J)
<u>b)</u>
<u>Identify the unknown: </u>
The charge and energy stored if the capacitors are connected in parallel
<u>Set Up the Problem: </u>
Capacitance of a parallel combination:
![C_{p} =C_{1} +C_{2} +C_{3}](https://tex.z-dn.net/?f=C_%7Bp%7D%20%3DC_%7B1%7D%20%2BC_%7B2%7D%20%2BC_%7B3%7D)
![C_{p} =2+7.4=9.4*10^-6F](https://tex.z-dn.net/?f=C_%7Bp%7D%20%3D2%2B7.4%3D9.4%2A10%5E-6F)
Capacitance of a parallel combination is given by
![C_{p} =\frac{Q}{V}](https://tex.z-dn.net/?f=C_%7Bp%7D%20%3D%5Cfrac%7BQ%7D%7BV%7D)
Then the charge stored in the parallel combination is
![Q=C_{p} V](https://tex.z-dn.net/?f=Q%3DC_%7Bp%7D%20V)
Energy stored in the parallel combination is:
![U_{c}=\frac{1}{2} V^2C_{p}](https://tex.z-dn.net/?f=U_%7Bc%7D%3D%5Cfrac%7B1%7D%7B2%7D%20V%5E2C_%7Bp%7D)
<u>Solve the Problem: </u><em> </em>
![Q=9.4*10^-6*9=8.46*10^-5C\\\\U_{c} =\frac{1}{2}*9^{2} *9.4*10^-6=3.81*10^-4J](https://tex.z-dn.net/?f=Q%3D9.4%2A10%5E-6%2A9%3D8.46%2A10%5E-5C%5C%5C%5C%5CU_%7Bc%7D%20%3D%5Cfrac%7B1%7D%7B2%7D%2A9%5E%7B2%7D%20%2A9.4%2A10%5E-6%3D3.81%2A10%5E-4J)