All questions refer to an RC circuit: resistance R andcapacitor C are connected

Question

All questions refer to an RC circuit: resistance R andcapacitor C are connected in series to a DC battery (withdifference of potential V) and a switch. Initially, the switch isopen and the capacitor has no charge. At t = 0, the switch isclosed.
a) How many time constants will it take before the charge onthe capacitor is within 1.24% of itsmaximum value? b) After the time you found in part a, what is the current inthe circuit, in terms of the maximum current Imax? All questions refer to an RC circuit: resistance R andcapacitor C are connected in series to a DC battery (withdifference of potential V) and a switch. Initially, the switch isopen and the capacitor has no charge. At t = 0, the switch isclosed.
a) How many time constants will it take before the charge onthe capacitor is within 1.24% of itsmaximum value? b) After the time you found in part a, what is the current inthe circuit, in terms of the maximum current Imax?

Explanation / Answer

V = V0 (1 - e-t/RC) Q = Q0 (1 -e-t/RC)      since Q = CV V / V0 = 1 - e-t/RC = .9876 e-t/RC = .0124 t / (RC) = 4.39   taking the log of bothsides t = 4.39   time constants since R C isthe time constant I = I0 e-t/RC I / I0 = e-4.39 since t =4.39 R C I /I0 = .0124 I / I0 = e-4.39 since t =4.39 R C I /I0 = .0124

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---