# Answer in Electric Circuits for Nike #159173

Explanations & Calculations

• According to the usual equation for capacitors — “small Q=CV”— generated potential between the plates of “small 2mu F” capacitor is

“qquadqquadnbegin{aligned}nsmall V_2&= small frac{120mu C}{2 mu F}=60,Vnend{aligned}”

• That of the “small 4mu F” capacitor is

“qquadqquadnbegin{aligned}nsmall V_4&= small frac{120 mu C}{4 mu F}=30,Vnend{aligned}”

• For “bold{small 2mu F}”

1) Potential on (+) plate = +30V and on (-) plate= -30V : “bold{small Delta V=60V}”

2) charge on (+) plate = “bold{small +60 mu C}” and on (-) plate = “bold{small -60 mu F}”

• For “bold{small 4mu F}”

1)+15V and -15V

2) “bold{small 60mu C ,,text{and},, 60mu C}”

• Now the greater potential is with the low valued capacitor.
• When connected (+) to (+) and (-) to (-), what happens is electrons move from the lower (+) plate to the higher (+) plate and from the higher (-) plate to the lower (-) plate until all the like plates (+/+ and -/-) become equipotential plates.
• Equal amounts of electrons move in each connection such that the ultimate potentials are “bold{small +V ,text{and},-V}”

• Electron-wise calculation from plate to plate is somewhat difficult and the easy method is to think some “delta q” amount of charges move from high potential to low potential (30V “small to” 15V) until potentials get equal.
• Then,

“qquadqquadnbegin{aligned}nsmall V_2&= V_4\nsmall frac{120mu C-delta q}{2mu F}&= small frac{120mu C+delta q}{4mu F}\nsmall delta q&= small 40mu Cnend{aligned}”

• Now the final potentials are,

“qquadqquadnbegin{aligned}nsmall V_{2new}&= small frac{(120-40)mu C}{2mu F}=bold{40,V}cdots(60Vto40V)\nsmall V_{4new}&= small frac{(120+40)mu C}{4mu F}=bold{40,V}cdots(30Vto40V)nend{aligned}”

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