Consider a series circuit containing a resistor of resistance R and a capacitor of capacitance C connected to a source of EMF E with negligible internal resistance. The wires are also assumed to have zero resistance. Initially, the switch is open and the capacitor discharged.
Let us try to understand the processes that take place after the switch is closed. The charge of the capacitor, the current in the circuit, and, correspondingly, the voltages across the resistor and the capacitor, will be changing. Note that at any moment in time during the life of our circuit, Kirchhoff's loop rule holds and indeed, it is helpful: E - V_R - V_C = 0, where V_R is the voltage across the resistor, and V_C is the voltage across the capacitor.

Given that:
q(t) = C*E(1-e^(-t/RC)

The Problem states:
Find the time t_2 it would take the charge of the capacitor to reach 99.9% of its maximum value given that R=12 Ohms and C = 500 * 10^ -6 F.

Express your answer numerically in seconds. Use three significant figures.

As a hint is given that:
1. find the time t_1 that it takes the charge of the capacitor to reach 99.9% of its maximum value.

To do 1. it says to:
2. What is the maximum charge on the capacitor? Set q(t) = to 99.9% of this value and solve for the corresponding time.

Please see the attached file for detailed solution.

Learning Goal: To understand the dynamics of a series R-C circuit.
Consider a series circuit containing a resistor of resistance and a capacitor of capacitance connected to a source of EMF with negligible internal resistance. The wires are also assumed to have zero resistance. Initially, the switch is open and the capacitor discharged.
Let us try to understand the processes that take place ...

Solution Summary

It finds the time for the charge of the capacitor to reach 99.9% maximum in a RC circuit.

Please help with the following problem. Step by step calculations are given.
An L-C circuit consists of a 60.0 mH inductor and 250 µF capacitor. The initial Charge in the capacitor is 6.00 µC and initial current in the inductor is zero.
a) What is the maximum voltage across the capacitor?
b) What is the maximum current

A capacitor is used in the electronic flash unit of a camera. A small battery with a constant voltage of 6 V is used to charge the capacitor with a constant current of 10 microamperes. How long does it take to charge the capacitor when C = 10 microfarads? My Answer:
V=6V
i=10mA
C=10microF
Wc=1/2CV^2*(t)
Wc=1/2(10^-5)6^2*(t

Please helps answer the following questions.
A 1 kOhm resistor is in series with a 1 muF capacitor.
a. What is the RC time constant of resistor-capacitor pair?
b. The 1 muF capacitor is charged from a 10 V battery via the 1 kOhm resistor. How long does it take for the voltage on the capacitor to reach 6.3 volts?
c.

(Please see the attachment for detailed problem)
1) In a circuit shown below it took capacitor 0.138 seconds to discharge from its maximumcharge Qmax to half of that maximumcharge once the battery was removed.
a) How much time would it take that capacitor to discharge from its maximumcharge to 1/16th of that maximu

A circuit contains an electromotive force [E(t)], a capacitor with capacitance of C Farads, and a resistor with a resistance of R ohms. The voltage drop across the capacitor is Q/C where Q is the charge in Coulombs, so Kirchoff's Law gives
R * I + Q/C = E(t)
But I = dQ/dt, so
R * dQ/dt + 1/C * Q = E(t)
If the resista

I have a question that I need a little help with.
A 5.0 uf capacitor is connected to a 3.5 uf capacitor, and both of them are connected to a 6 volt battery.
1) what is the charge on each capacitor? What is the voltage on each capacitor?
2) With the battery still connected, the 3.5 uf cap is accidentally shorted out. As

If a capacitor with a capacitance of 0.000005 farads is wired in a circuit with a total resistance of 5000 ohms (the standard unit of electrical resistance), how long must the capacitor be wired to a source voltage to reach 50% of its maximumcharge?
(The Hint was: Begin by expressing q as 0.5Q)