A series RC circuit,which is made from a battery,a switch,a resistor,and a 5-μF capacitor,has a time constant of 8 ms.If an additional 7-μF is added in series to the 5-μF capacitor,what is the resulting time constant?
A) 11.2 ms
B) 4.7 ms
C) 0.5 ms
D) 13.7 ms
E) This cannot be found without the value of the resistance being given.

Question

A series RC circuit,which is made from a battery,a switch,a resistor,and a 5-μF capacitor,has a time constant of 8 ms.If an additional 7-μF is added in series to the 5-μF capacitor,what is the resulting time constant?
A) 11.2 ms
B) 4.7 ms
C) 0.5 ms
D) ​13.7 ms
E) ​This cannot be found without the value of the resistance being given.

Quizplus · Accepted Answer

The time constant τ = RC. When capacitors are in series, the total capacitance C_total is given by 1/C_total = 1/C1 + 1/C2. For 5-μF and 7-μF in series, C_total = 2.917 μF. The original time constant is 8 ms with 5-μF, so R = τ/C = 8 ms / 5 μF. The new time constant τ' = R * C_total = (8 ms / 5 μF) * 2.917 μF = 4.7 ms.

A Series RC Circuit,which Is Made from a Battery,a Switch,a