A 2.0-μF capacitor and a 4.0-μF capacitor are connected in series across an 8.0-V potential source.What is the charge on the 2.0-μF capacitor?
A)2.0 μC
B)4.0 μC
C)12 μC
D)11 μC
E)25 μC

Question

Quizplus · Accepted Answer

When capacitors are connected in series, the charge is the same on both capacitors.

First, we can calculate the equivalent capacitance:

Ceq = (C1 * C2) / (C1 + C2) 
Ceq = (2.0 μF * 4.0 μF) / (2.0 μF + 4.0 μF) 
Ceq = 8/6 μF 
Ceq = 4/3 μF

Now, we can use the equation Q = C * V to find the charge on the capacitors:

Q = Ceq * V 
Q = (4/3) μF * 8.0 V 
Q = 32/3 μC

Since the charge is the same on both capacitors, the charge on the 2.0-μF capacitor is:

Q = (2.0 μF / Ceq) * (32/3 μC) 
Q = (2.0 μF / (4/3) μF) * (32/3 μC) 
Q = 16/3 μC

Therefore, the answer is D) 11 μC.

A 20-μF Capacitor and a 4