At t = 0 the switch S is closed with the capacitor uncharged.If C = 50 μF,ε = 20 V,and R = 4.0 kΩ,what is the charge on the capacitor when I = 2.0 mA?
A)360 μC
B)480 μC
C)240 μC
D)600 μC
E)400 μC

Question

At t = 0 the switch S is closed with the capacitor uncharged.If C = 50 μF,ε = 20 V,and R = 4.0 kΩ,what is the charge on the capacitor when I = 2.0 mA? 
A)360 μC 
B)480 μC 
C)240 μC 
D)600 μC 
E)400 μC

Quizplus · Accepted Answer

The charge on the capacitor is given by the formula:
Q = C × Vc
where Vc is the voltage across the capacitor.

Using Kirchhoff's loop rule, we can write:
ε - IR - Vc = 0
=> Vc = ε - IR

At t = 0, the capacitor is uncharged, so Vc = 0.
When the switch is closed, the current flowing through the circuit is:
I = ε / R = 20 V / 4.0 kΩ = 5.0 mA

After a time t, the charge on the capacitor can be written as:
Q = C × Vc = C × (ε - IR)

When I = 2.0 mA, we can write:
Q = C × (ε - IR) = 50 μF × (20 V - 2.0 mA × 4.0 kΩ) = 600 μC

Therefore, the answer is (D) 600 μC.

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