21.6 DC Circuits Containing Resistors and Capacitors

When is the potential difference across a capacitor an emf?

An uncharged capacitor C is connected in series (with a switch) to a resistor R₁ and a voltage source E. Assume E = 24 V, R₁ = 1.2 kΩ and C = 1 mF.

1. What will be the current through the circuit as the switch is closed? Draw a circuit diagram and show the direction of current after the switch is closed. How long will it take for the capacitor to be 99% charged?
2. After full charging, this capacitor is…

The timing device in an automobile’s intermittent wiper system is based on an $\text{RC}$ time constant and utilizes a $0 . \text{500}-\mu\text{F}$ capacitor and a variable resistor. Over what range must $R$ be made to vary to achieve time constants from 2.00 to 15.0 s?

The duration of a photographic flash is related to an $\text{RC}$ time constant, which is $0 . \text{100 }\mu\text{s}$ for a certain camera. (a) If the resistance of the flash lamp is $0 . \text{0400} \Omega$ during discharge, what is the size of the capacitor supplying its energy? (b) What is the time constant for charging the capacitor, if the charging resistance is $\text{800} \text{ k}\Omega$?

After two time constants, what percentage of the final voltage, emf, is on an initially uncharged capacitor $C$, charged through a resistance $R$?

A heart defibrillator being used on a patient has an $\text{RC}$ time constant of 10.0 ms due to the resistance of the patient and the capacitance of the defibrillator. (a) If the defibrillator has an $8 . \text{00}-\mu\text{F}$ capacitance, what is the resistance of the path through the patient? (You may neglect the capacitance of the patient and the resistance of the defibrillator.) (b) If the initial voltage is 12.0 kV, how long…

Using the exact exponential treatment, find how much time is required to charge an initially uncharged 100-pF capacitor through a $\text{75} . 0 -\text{M} \Omega$ resistor to 90.0% of its final voltage.

If you wish to take a picture of a bullet traveling at 500 m/s, then a very brief flash of light produced by an $\text{RC}$ discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one $\text{RC}$ constant is acceptable, and given that the flash is driven by a $\text{600}-\mu\text{F}$ capacitor, what is the resistance in the flash tube?

A $\text{160}-\mu\text{F}$ capacitor charged to 450 V is discharged through a $31 . \text{2}-\text{k} \Omega$ resistor. (a) Find the time constant. (b) Calculate the temperature increase of the resistor, given that its mass is 2.50 g and its specific heat is $1 . \text{67} \frac{\text{kJ}}{\text{kg} \cdot º\text{C}}$, noting that most of the thermal energy is retained in the short time of the discharge. (c) Calculate the new resistance, assuming it is pure carbon. (d) Does this change in resistance seem s…

A circuit has a voltage source producing $1.00 \times 10^{2} \text{V}$ and a $2.50 \times 10^{3} \Omega$ resistor. (a) If the circuit contains nothing else, how much power is dissipated by the resistor? (b) A second $2.50 \times 10^{3} \Omega$ resistor is added in parallel to the first resistor. Now how much power is dissipated by the resistors? (c) Now place the two resistors in series. How much power is dissipated by the resistors? (d) Why would a parallel arrangement of r…