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 by a capacitor can be calculated using the formula:
E = (1/2) * C * V^2

At t=0, the capacitor is uncharged, so the initial voltage across the capacitor is 0.

Using Ohm's law, we can find the voltage across the resistor:
V = I * R
V = 2.0 mA * 5.0 kΩ
V = 10 V

Now, we can find the voltage across the capacitor:
V_C = ε - V
V_C = 50 V - 10 V
V_C = 40 V

Using the formula for energy stored by a capacitor, we get:
E = (1/2) * C * V^2
E = (1/2) * 40 μF * (40 V)^2
E = 32 mJ

Therefore, the answer is choice C.

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