The RC Time Constant

As you have seen, when a capacitor charges or discharges through a resistance, a certain time is required for the capacitor to charge fully or discharge fully. The voltage across a capacitor cannot change instantaneously, because a finite time is required to move charge from one point to another.

The arte at which the capacitor charges or discharges is determined by the time constant of the circuit.

The time constant of a series RC circuit is a time interval that equals the product of the resistance and the capacitance.

The time constant is symbolized by  , and the formula is as follows

 = RC

Recall that I = Q/t. The current is the amount of charge moved in a given time. When the resistance is increased, the charging current is reduced, thus increasing the charging time of the capacitor.

When the capacitance is increased, the amount of charge increases; thus, for the same current, more time is required to charge the capacitor.

Example 5.2 A series RC circuit has a resistance of 1 M and a capacitance of 5 F. What is the

Voltage and Current in a Capacitor during charging

Voltage across the

capacitor

Current through the capacitor

time time

Problem Set No. 11 CAPACITOR AND CAPACITANCE

1. Two capacitors connected in parallel across a 250-V mains have charges of 3,000 µC and 5,000

C, respectively. Find the total capacitance of the combination.

a. 32 µF

3. The equivalent capacitance of two capacitors in series is 2.4 F. If one of the capacitors has a capacitance of 4 F, what is the capacitance of the other?

a. 2 µF b. 4 µF c. 6 µF d. 8µF

4. Three capacitors having capacitance of 4 F , 6 F and 8 F respectively are connected in series.

Find the equivalent capacitance of the combination.

a. 1.08 µF b. 2.84 µF c. 1.84 µF d. 4.84 µF

5. The energy stored in a 0.125 F capacitor is 50 J, solve for the charge accumulated.

a. 3.54 mC b. 5.34 mC c. 6.23 mC d. 8,45 mC

6. A certain capacitor is charged at 48 volts after its stored energy is 5.76 x 10^-2 joules. What is the capacitance of the capacitor?

a. 25 µF b. 50 µF c. 75 µF

d. 89 µF

7. Calculate the capacitance between two plates each of which is 100 cm² and 2 mm apart in air.

a. 44.27 nF b. 48.90 nF c. 56.84 nF d. 76.43 nF

8. A capacitor whose plates is 20 cm x 3.0 cm and is separated by a 1.0-mm air gap is connected across a 12-V battery. Determine the charge accumulated on each plate after a long time.

a. 43.89 nC b. 56.32 nC c. 63.75 nC d. 89.56 nC

9. Three capacitors A, B, and C are charged as follows: A: 10F, 100 volts; B: 15 F, 150 volts; C:

25 F, 200 volts. They are then connected in parallel with terminals of like polarity together.

What is the voltage across the combination?

a. 165 V b. 175 V c. 185 V d. 195 V

10. A given capacitor has a capacitance of 100 F. Calculate its elastance.

a. 1,000 D b. 10,000 D c. 100,000 D d. 1,000,000 D

11. Three capacitors of 5 F , 10 F and 15 F respectively are connected in series across a 100-V supply. Solve for the voltage across the 15-F capacitor.

a. 18.2 V b. 19.6 V c. 20.7 V d. 25.4 V

Objective Test No. 5 CAPACITOR AND CAPACITANCE

1. Which of the following statement(s) accurately describes a capacitor?

The plates are conductive.

The dielectric is an insulator between the plates.

Constant dc flows through a fully charged capacitor.

A practical capacitor stores charge indefinitely when disconnected from the source.

2. The capacity of a condenser is proportional to ___________.

area of its plates volume of its plates

the specific resistance of the plate material the temperature coefficient of the plate material

3. The capacity of the capacitor is inversely proportional to ________.

the temperature of the dielectric the material of the dielectric the thickness of the dielectric

the permeability of the material and inductance 4. The capacitors in series have the same _______.

voltage capacity charge energy loss

5. The capacitors are named according to the _______ used.

material of the plate dielectric used enclosures used voltage

6. When one of the following statements is true?

There is current through the dielectric of a charging capacitor.

When a capacitor is connected to a DC voltage source, it will charge to the value of the source.

An ideal capacitor can be discharged by disconnecting it from the voltage source.

7. A capacitance of 0.01 F is larger than 0.00001 F

100,000 pF

1000 pF all of the above

8. When the voltage across a capacitor is increased, the stored charge increases

decreases remains constant fluctuates

9. When the voltage across a capacitor is doubled, the stored charge stays the same

is halved

increases by four doubles

10. The voltage rating of a capacitor is increased by decreasing plate area

increasing plate separation increasing the plate area a and b

11. The capacitance value is increased by decreasing plate area

increasing plate separation decreasing plate separation increasing plate area

12. An uncharged capacitor and a resistor are connected in series with a switch and a 12-V battery.

At the instant the switch is closed, the voltage across the capacitor is 12 V

6 V

24 V 0 V

13. In Question 12, the voltage across the capacitor when it is fully charged is 12 V

6 V 24 V -6 V

14. An ohmmeter is connected across a discharged capacitor and the needle stabilizes at approximately 50 k. The capacitor is

good charged too large

leaky

15. A good capacitor has a __________ resistance.

negligible very high negative none of these

16. A capacitor opposes any change in __________.

current voltage Resistance flux

17. The capacitance of a capacitor is directly proportional to area of its plate

19. A capacitor consists of two _________

insulators separated by a conductor.

conductors separated by an insulator conductors

insulators

20. Capacitors designed to be used in places where a high dielectric breakdown voltage is important .

22. The capacitance of a capacitor is NOT affected by _____.

type of dielectric material distance between plates area of the plates

type of material used in the plates

23. The capacitor stores the electricity in the shape of _____.

dynamic charge static charge current electricity molecules

24. Capacitors are used in electric circuits to ____________.

store energy

introduce a voltage drop

produce a low opposition path to high frequencies all of these

Unit 6