# 21.6 Dc circuits containing resistors and capacitors  (Page 5/10)

 Page 5 / 10

When is the potential difference across a capacitor an emf?

Only when the current being drawn from or put into the capacitor is zero. Capacitors, like batteries, have internal resistance, so their output voltage is not an emf unless current is zero. This is difficult to measure in practice so we refer to a capacitor’s voltage rather than its emf. But the source of potential difference in a capacitor is fundamental and it is an emf.

## Phet explorations: circuit construction kit (dc only)

An electronics kit in your computer! Build circuits with resistors, light bulbs, batteries, and switches. Take measurements with the realistic ammeter and voltmeter. View the circuit as a schematic diagram, or switch to a life-like view.

## Test prep for ap courses

A battery is connected to a resistor and an uncharged capacitor. The switch for the circuit is closed at t = 0 s.

1. While the capacitor is being charged, which of the following is true?

1. Current through and voltage across the resistor increase.
2. Current through and voltage across the resistor decrease.
3. Current through and voltage across the resistor first increase and then decrease.
4. Current through and voltage across the resistor first decrease and then increase.
2. When the capacitor is fully charged, which of the following is NOT zero?

1. Current in the resistor.
2. Voltage across the resistor.
3. Current in the capacitor.
4. None of the above.

An uncharged capacitor C is connected in series (with a switch) to a resistor R 1 and a voltage source E . Assume E = 24 V, R 1 = 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 connected in series to another resistor, R 2 = 1 kΩ. What will be the current in the circuit as soon as it’s connected? Draw a circuit diagram and show the direction of current. How long will it take for the capacitor voltage to reach 3.24 V?

(a) 20 mA, [link] , 5.5 s; (b) 24 mA, [link] , 2 s

## Section summary

• An $\text{RC}$ circuit is one that has both a resistor and a capacitor.
• The time constant $\tau$ for an $\text{RC}$ circuit is $\tau =\text{RC}$ .
• When an initially uncharged ( ${V}_{0}=0$ at $t=0$ ) capacitor in series with a resistor is charged by a DC voltage source, the voltage rises, asymptotically approaching the emf of the voltage source; as a function of time,
$V=\text{emf}\left(1-{e}^{-t/\text{RC}}\right)\text{(charging).}$
• Within the span of each time constant $\tau$ , the voltage rises by 0.632 of the remaining value, approaching the final voltage asymptotically.
• If a capacitor with an initial voltage ${V}_{0}$ is discharged through a resistor starting at $t=0$ , then its voltage decreases exponentially as given by
$V={V}_{0}{e}^{-t/\text{RC}}\text{(discharging).}$
• In each time constant $\tau$ , the voltage falls by 0.368 of its remaining initial value, approaching zero asymptotically.

## Conceptual questions

Regarding the units involved in the relationship $\tau =\text{RC}$ , verify that the units of resistance times capacitance are time, that is, $\Omega \cdot F=s$ .

what is angular velocity
Why does earth exert only a tiny downward pull?
hello
Islam
Why is light bright?
an 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit
thanks so much. i undersooth well
what is physics
is the study of matter in relation to energy
Kintu
a submersible pump is dropped a borehole and hits the level of water at the bottom of the borehole 5 seconds later.determine the level of water in the borehole
what is power?
power P = Work done per second W/ t. It means the more power, the stronger machine
Sphere
e.g. heart Uses 2 W per beat.
Rohit
A spherica, concave shaving mirror has a radius of curvature of 32 cm .what is the magnification of a persons face. when it is 12cm to the left of the vertex of the mirror
did you solve?
Shii
1.75cm
Ridwan
my name is Abu m.konnek I am a student of a electrical engineer and I want you to help me
Abu
the magnification k = f/(f-d) with focus f = R/2 =16 cm; d =12 cm k = 16/4 =4
Sphere
what do we call velocity
Kings
A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa
hi
Godfred
Godfred
If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
the same behavior thru the prism out or in water bud abbot
Ju
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
Anurag
What was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?
Jaydie
29/20 ? maybes
Ju
In what ways does physics affect the society both positively or negatively
how can I read physics...am finding it difficult to understand...pls help
try to read several books on phy don't just rely one. some authors explain better than other.
Ju
And don't forget to check out YouTube videos on the subject. Videos offer a different visual way to learn easier.
Ju
hope that helps
Ju