At t = 0 the switch S is closed with the capacitor uncharged. If C = 40 μF, ε = 50 V, and R = 5.0 kΩ, how much energy is stored by the capacitor when I = 2.0 mA?
A)20 mJ
B)28 mJ
C)32 mJ
D)36 mJ
E)40 mJ

Question

At t = 0 the switch S is closed with the capacitor uncharged. If C = 40 μF, ε = 50 V, and R = 5.0 kΩ, how much energy is stored by the capacitor when I = 2.0 mA? 
A)20 mJ 
B)28 mJ 
C)32 mJ 
D)36 mJ 
E)40 mJ

Quizplus · Accepted Answer

The energy stored in a capacitor is given by:
$E=\frac{1}{2}CV^2$
We can solve for V using Ohm's Law:
$V=IR$
$V=(2.0 mA)(5.0 kΩ)=10 V$
Substituting this into the formula for energy stored, we get:
$E=\frac{1}{2}(40 μF)(10 V)^2=32 mJ$
Therefore, the answer is C) 32 mJ.

At T = 0 the Switch S Is Closed with the Capacitor