Three capacitors are connected in parallel. Each has platearea A = 4.00×10 -2 m

Question

Three capacitors are connected in parallel. Each has platearea A = 4.00×10-2m2 andplate spacing d = 2.20×10-3m.
1. What must be thespacing of a single capacitor of plate area A if its capacitanceequals that of the parallel combination? 2. What must bethe spacing if the three capacitors are connected inseries? Three capacitors are connected in parallel. Each has platearea A = 4.00×10-2m2 andplate spacing d = 2.20×10-3m.
1. What must be thespacing of a single capacitor of plate area A if its capacitanceequals that of the parallel combination? 2. What must bethe spacing if the three capacitors are connected inseries? 2. What must bethe spacing if the three capacitors are connected inseries?

Explanation / Answer

Three capacitors are connected in parallel. Each has platearea A = 4.00×10-2m2 andplate spacing d = 2.20×10-3m.


1. What must be thespacing of a single capacitor of plate area A if its capacitanceequals that of the parallel combination?


effective capacity when they are connected inparallel=3Ao/d=3*4.00×10-2*8.85*10-12/2.20×10-3=48.27*10-11F
now spacing when single capacitor having capacitance48.27*10-11 =Ao/C=
4.00×10-2*8.85*10-12/48.27*10-11=0.7333*10-3m

2. What must bethe spacing if the three capacitors are connected in series?

effectivecapacity when they are connected in series=C/3=Ao/3d=4.00×10-2*8.85*10-12/3*2.20×10-3=5.3636*10-11F

nowspacing when single capacitor havingcapacitance5.3636*10-11=Ao/C=
4.00×10-2*8.85*10-12/5.3636*10-11=6.60*10-3m


2. What must bethe spacing if the three capacitors are connected in series?

effectivecapacity when they are connected in series=C/3=Ao/3d=4.00×10-2*8.85*10-12/3*2.20×10-3=5.3636*10-11F

nowspacing when single capacitor havingcapacitance5.3636*10-11=Ao/C=
4.00×10-2*8.85*10-12/5.3636*10-11=6.60*10-3m

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