A circuit contains a 6.0-V battery,a 4.0-Ω resistor,a 0.60-µF capacitor,an ammeter,and a switch in series.What will be the charge on the capacitor 10 min after the switch is closed?
A)zero
B)0.10 μC
C)3.6 μC
D)2.4 μC

Question

A circuit contains a 6.0-V battery,a 4.0-Ω resistor,a 0.60-µF capacitor,an ammeter,and a switch in series.What will be the charge on the capacitor 10 min after the switch is closed? 
A)zero 
B)0.10 μC 
C)3.6 μC 
D)2.4 μC

Quizplus · Accepted Answer

After a long time, the capacitor will be fully charged and no current will flow through the circuit. The time constant of the circuit is given by τ = RC = 4.0 Ω × 0.60 μF = 2.4 × 10^-6 s. After 10 minutes, which is 600 seconds, the capacitor will have charged to approximately 99.3% of its maximum voltage, given by Vmax = 6.0 V. The charge on the capacitor Q is given by Q = CV, where C is the capacitance of the capacitor. Thus, Q = (0.60 μF)(0.993)(6.0 V) = 3.6 μC. Therefore, the answer is (C).

A Circuit Contains a 6