In the figure below(Figure 1) , the top left capacitor and top right capacitor h
ID: 1769127 • Letter: I
Question
In the figure below(Figure 1) , the top left capacitor and top right capacitor has 3.56microF , the middle capacitor has 3.02microF , and the bottom capacitor has 7.06microF , and the voltage across ab is 89.8V . What is the equivalent capacitance of this circuit? What is the charge and voltage on the top left capacitor? What is the charge and voltage on the top right capacitor? What is the charge and voltage on the middle capacitor? What is the charge and voltage on the bottom capacitor? In the figure below(Figure 1), the top left capacitor and top right capacitor has 3.56MuF , the middle capacitor has 3.02MuF , and the bottom capacitor has 7.06MuF , and the voltage across ab is 89.8V.Explanation / Answer
a)
equivalent capacitance
Both top left and Right capacitors are in series
1/C =1/3.56 +1/3.56
C=1.78 uF
1.78 uF and 3.02 uF are in parallel
1.78+3.02=4.8 uF
4.8 uF and 7.06 uF are in series ,so equivalent capacitance
1/Ceq =1/4.8 +1/7.06
Ceq=2.86 uF
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Total charge stored
Q=Ceq*V =2.86*89.8=256.6 uC
Charge on top left and right capacitors is
Qleft=Qright=Q*(1.78/1.78+3.02) =256.6*(1.78/4.8) =95.2 uC
Charge on middle capacitor
Qmiddle=Q-Qleft =161.4 uC
Charge on bottom capacitor
Qbottom=Q=256.6 uC
Voltage across each capacitor
Vleft=Vright=Qleft/C =95.2/3.56 =26.7 Volts
Vmiddle=Qmiddle/C =161.4/3.02 =53.4 Volts
Vbottom=Qbottom/C =256.6/7.06 =36.4 Volts
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b)
Qright=95.2 uC
Vright=26.7 Volts
c)
Qleft=95.2 uC
Vleft=26.7 Volts
d)
Qmiddle=161.4 uC
Vmiddle=53.4 Volts
e)
Qbottom=256.6 uC
Vbottom=36.4 Volts