To store a total of 0.040 J of energy in the two identical capacitors shown, each should have a capacitance of:
A)0.50 $\mu$F
B)1.0 $\mu$F
C)1.5 $\mu$F
D)2.0$\mu$F
E)4.0 $\mu$F

Question

To store a total of 0.040 J of energy in the two identical capacitors shown, each should have a capacitance of: 
A)0.50 $\mu$F 
B)1.0 $\mu$F 
C)1.5 $\mu$F 
D)2.0$\mu$F 
E)4.0 $\mu$F

Quizplus · Accepted Answer

The energy stored in a capacitor is given by the formula: 
E = (1/2)CV^2, where E is the energy in joules, C is the capacitance in farads, and V is the potential difference across the capacitor in volts. 
In this case, we know that E = 0.040 J and we have two identical capacitors connected in parallel, so the total capacitance is twice the capacitance of each individual capacitor. 
So, we can rearrange the formula to solve for C: 
C = (2E)/(V^2) 
We don't know the voltage across the capacitors, but we can assume it is the same as the voltage of the battery (10 V). 
Plugging in the numbers, we get: 
C = (2 x 0.040 J)/(10 V)^2 = 0.001 F = 1.0 μF 
Therefore, the answer is choice B) 1.0 μF.

To Store a Total of 0 μ\muμ F B)10 μ\muμ F C)15 μ\muμ

To Store a Total of 0 $\mu$ F
B)10 $\mu$ F
C)15 $\mu$