 #1
Shreya
 170
 63
 Homework Statement:

Lets consider 2 parallel plate capacitors ##C_1## and ##C_2##.
##C_1## has plate area twice of the ##C_2##, but same width. If both stores equal charge ##Q##. Which one has more energy?
 Relevant Equations:

$$U = (Volume) \frac 1 2 \epsilon E^2$$
$$U= \frac {Q^2}{2C}$$
$$U= \frac 1 2 CV^2$$
I developed three arguments to answer this question. Argument no 2 seems to be wrong, but I cant figure out why. I know one/more of my arguments are flawed. Please be kind to help me figure this out.
Argument 1) Since they have same charge on them, the ##E## between them must be same. The one with more volume ##C_1## must have more energy, according to the first equation.
Argument 2) According to equation 1, ##C_1## must have lesser Energy that ##C_2##, due to higher capacitance. (Refer second equation)
Argument 3) Due to same width and same ##E##. they must have same ##V## between them. According to equation 3, ##C_1## must have more Energy
Thanks for your time!
Argument 1) Since they have same charge on them, the ##E## between them must be same. The one with more volume ##C_1## must have more energy, according to the first equation.
Argument 2) According to equation 1, ##C_1## must have lesser Energy that ##C_2##, due to higher capacitance. (Refer second equation)
Argument 3) Due to same width and same ##E##. they must have same ##V## between them. According to equation 3, ##C_1## must have more Energy
Thanks for your time!