ConcepTest 21.1ConcepTest 21.1 Connect the Battery Connect the Battery

Which is the correct way to Which is the correct way to

light the lightbulb with the light the lightbulb with the battery?battery?

4) all are correct

5) none are correct

1) 3)2)

Current can only flow if there is a continuous connectioncontinuous connection from the negative terminal through the bulb to the positive terminal.

This is only the case for Fig. (3).

ConcepTest 21.1ConcepTest 21.1 Connect the Battery Connect the Battery

Which is the correct way to Which is the correct way to

light the lightbulb with the light the lightbulb with the battery?battery?

4) all are correct

5) none are correct

1) 3)2)

1) Ohm’s law is obeyed since the Ohm’s law is obeyed since the current still increases when V current still increases when V increasesincreases

2) Ohm’s law is not obeyedOhm’s law is not obeyed

3) this has nothing to do with Ohm’s this has nothing to do with Ohm’s lawlaw

ConcepTest 21.2ConcepTest 21.2 Ohm’s Law Ohm’s Law

You double the You double the voltagevoltage across a certain conductor across a certain conductor and you observe the and you observe the currentcurrent increases three times. What increases three times. What can you conclude?can you conclude?

1) Ohm’s law is obeyed since the Ohm’s law is obeyed since the current still increases when V current still increases when V increasesincreases

2) Ohm’s law is not obeyedOhm’s law is not obeyed

3) this has nothing to do with Ohm’s this has nothing to do with Ohm’s lawlaw

Ohm’s law, V = I RV = I R, states that the relationship between voltage and current is linearlinear. Thus for a conductor that obeys Ohm’s Law, the current must double when you double the voltage.

ConcepTest 21.2ConcepTest 21.2 Ohm’s Law Ohm’s Law

You double the You double the voltagevoltage across a certain conductor across a certain conductor and you observe the and you observe the currentcurrent increases three times. What increases three times. What can you conclude?can you conclude?

Follow-up:Follow-up: Where could this situation occur? Where could this situation occur?

ConcepTest 21.3aConcepTest 21.3a Wires IWires I

Two wires, Two wires, AA and and BB, are made of the , are made of the same metalsame metal and have and have equal lengthequal length, , but the resistance of wire but the resistance of wire AA is is four four timestimes the resistance of wire the resistance of wire BB. How . How do their diameters compare?do their diameters compare?

1) ddAA = 4 = 4 ddBB

2) ddAA = 2 = 2 ddBB

3) ddAA = = ddBB

4) 4) ddAA = 1/2 = 1/2 ddBB

5) 5) ddAA = 1/4 = 1/4 ddBB

The resistance of wire A is greater because its area is lessarea is less than wire B. Since areaarea is related to radiusradius (or diameter) squaredsquared, the diameter of diameter of AA must be two times less than must be two times less than BB.

ConcepTest 21.3aConcepTest 21.3a Wires IWires I

ALR

Two wires, Two wires, AA and and BB, are made of the , are made of the same metalsame metal and have and have equal lengthequal length, , but the resistance of wire but the resistance of wire AA is is four four timestimes the resistance of wire the resistance of wire BB. How . How do their diameters compare?do their diameters compare?

1) ddAA = 4 = 4 ddBB

2) ddAA = 2 = 2 ddBB

3) ddAA = = ddBB

4) 4) ddAA = 1/2 = 1/2 ddBB

5) 5) ddAA = 1/4 = 1/4 ddBB

ConcepTest 21.3bConcepTest 21.3b Wires II Wires II

A wire of resistance A wire of resistance RR is is stretched uniformly (keeping its stretched uniformly (keeping its volume constant) until it is twice volume constant) until it is twice its original length. What happens its original length. What happens to the resistance?to the resistance?

1) it decreasesit decreases by a factor 4by a factor 42) it decreasesit decreases by a factor 2by a factor 23) it stays the sameit stays the same4) it increases4) it increases by a factor 2by a factor 25) it increases5) it increases by a factor 4by a factor 4

Keeping the volume (= area x length) constant means that if the length is doubleddoubled, the area is halvedhalved.

Since , this increases the resistance by fourfour.

ConcepTest 21.3bConcepTest 21.3b Wires II Wires II

ALR

A wire of resistance A wire of resistance RR is is stretched uniformly (keeping its stretched uniformly (keeping its volume constant) until it is twice volume constant) until it is twice its original length. What happens its original length. What happens to the resistance?to the resistance?

1) it decreasesit decreases by a factor 4by a factor 42) it decreasesit decreases by a factor 2by a factor 23) it stays the sameit stays the same4) it increases4) it increases by a factor 2by a factor 25) it increases5) it increases by a factor 4by a factor 4

ConcepTest 21.4aConcepTest 21.4a Series Resistors ISeries Resistors I

9 V

Assume that the voltage of the battery Assume that the voltage of the battery is is 9 V9 V and that the three resistors are and that the three resistors are identicalidentical. What is the potential . What is the potential difference across each resistor?difference across each resistor?

1) 12 V

2) zero

3) 3 V

4) 4 V

5) you need to know the actual value of R

Since the resistors are all equalequal, the voltage will drop evenlyevenly across the 3 resistors, with 1/3 of 9 V across each one. So we get a 3 V drop3 V drop across each.

ConcepTest 21.4aConcepTest 21.4a Series Resistors ISeries Resistors I

9 V

Assume that the voltage of the battery Assume that the voltage of the battery is is 9 V9 V and that the three resistors are and that the three resistors are identicalidentical. What is the potential . What is the potential difference across each resistor?difference across each resistor?

1) 12 V

2) zero

3) 3 V

4) 4 V

5) you need to know the actual value of R

Follow-up:Follow-up: What would be the potential difference if What would be the potential difference if RR= = 1

ConcepTest 21.4bConcepTest 21.4b Series Resistors IISeries Resistors II

12 V

R1= 4 R2= 2

In the circuit below, what is the In the circuit below, what is the

voltage across voltage across R1??

1) 12 V

2) zero

3) 6 V

4) 8 V

5) 4 V

ConcepTest 21.4bConcepTest 21.4b Series Resistors IISeries Resistors II

12 V

R1= 4 R2= 2

In the circuit below, what is the In the circuit below, what is the

voltage across voltage across R1??

1) 12 V

2) zero

3) 6 V

4) 8 V

5) 4 V

The voltage drop across RThe voltage drop across R11 has has

to be twice as big as the drop to be twice as big as the drop

across across RR22.. This means that VV11 = =

8 V8 V and V2 = 4 V. Or else you

could find the current I = V/R =

(12 V)/(6 = 2 A, then use

Ohm’s Law to get voltages. Follow-up:Follow-up: What happens if the voltage is doubled? What happens if the voltage is doubled?

ConcepTest 21.5aConcepTest 21.5a Parallel Resistors IParallel Resistors I

In the circuit below, what is the In the circuit below, what is the

current through current through R1??

10 V

R1= 5

R2= 2

1) 10 A

2) zero

3) 5 A

4) 2 A

5) 7 A

The voltagevoltage is the samesame (10 V) across each resistor because they are in parallel. Thus, we can use Ohm’s Law, VV11 = I = I11 R R11 to find the

current II11 = 2 A = 2 A.

ConcepTest 21.5aConcepTest 21.5a Parallel Resistors IParallel Resistors I

In the circuit below, what is the In the circuit below, what is the

current through current through R1??

10 V

R1= 5

R2= 2

1) 10 A

2) zero

3) 5 A

4) 2 A

5) 7 A

Follow-up:Follow-up: What is the total current through the battery? What is the total current through the battery?

ConcepTest 21.5bConcepTest 21.5b Parallel Resistors IIParallel Resistors II1) increases

2) remains the same

3) decreases

4) drops to zero

Points P and Q are connected to a Points P and Q are connected to a battery of fixed voltage. As more battery of fixed voltage. As more resistors resistors RR are added to the parallel are added to the parallel circuit, what happens to the circuit, what happens to the total total currentcurrent in the circuit? in the circuit?

ConcepTest 21.5bConcepTest 21.5b Parallel Resistors IIParallel Resistors II1) increases

2) remains the same

3) decreases

4) drops to zero

As we add parallel resistors, the overall resistance of the circuit dropsresistance of the circuit drops. Since V = IR, and V is held constant by the battery, when resistance decreasesresistance decreases, the current current must increasemust increase.

Points P and Q are connected to a Points P and Q are connected to a battery of fixed voltage. As more battery of fixed voltage. As more resistors resistors RR are added to the parallel are added to the parallel circuit, what happens to the circuit, what happens to the total total currentcurrent in the circuit? in the circuit?

Follow-up:Follow-up: What happens to the current through each resistor? What happens to the current through each resistor?

ConcepTest 21.6aConcepTest 21.6a Short CircuitShort Circuit

Current flows through a Current flows through a lightbulb. If a wire is now lightbulb. If a wire is now connected across the connected across the bulb, what happens?bulb, what happens?

1) all the current continues to flow through all the current continues to flow through the bulbthe bulb

2) half the current flows through the wire, half the current flows through the wire, the other half continues through the the other half continues through the bulbbulb

3) all the current flows through the wire all the current flows through the wire4) none of the abovenone of the above

The current divides based on the ratio of the resistances. If one of the resistances is zerozero, then ALLALL of the current will flow through that path.

ConcepTest 21.6aConcepTest 21.6a Short CircuitShort Circuit

Current flows through a Current flows through a lightbulb. If a wire is now lightbulb. If a wire is now connected across the connected across the bulb, what happens?bulb, what happens?

1) all the current continues to flow through all the current continues to flow through the bulbthe bulb

2) half the current flows through the wire, half the current flows through the wire, the other half continues through the the other half continues through the bulbbulb

3) all the current flows through the wire all the current flows through the wire4) none of the abovenone of the above

Follow-up:Follow-up: Doesn’t the wire have SOME resistance? Doesn’t the wire have SOME resistance?

ConcepTest 21.6bConcepTest 21.6b Short Circuit IIShort Circuit II

Two lightbulbs A and B are Two lightbulbs A and B are connected in series to a connected in series to a constant voltage source. constant voltage source. When a wire is connected When a wire is connected across B, bulb A will:across B, bulb A will:

1) glow brighter than beforeglow brighter than before

2) glow just the same as beforeglow just the same as before

3) glow dimmer than beforeglow dimmer than before

4) go out completely4) go out completely

5) explode5) explode

Since bulb B is bypassed by the wire, the total resistance of the circuit total resistance of the circuit decreasesdecreases. This means that the current current through bulb A increasesthrough bulb A increases.

ConcepTest 21.6bConcepTest 21.6b Short Circuit IIShort Circuit II

Two lightbulbs A and B are Two lightbulbs A and B are connected in series to a connected in series to a constant voltage source. constant voltage source. When a wire is connected When a wire is connected across B, bulb A will:across B, bulb A will:

1) glow brighter than beforeglow brighter than before

2) glow just the same as beforeglow just the same as before

3) glow dimmer than beforeglow dimmer than before

4) go out completely4) go out completely

5) explode5) explode

Follow-up:Follow-up: What happens to bulb B? What happens to bulb B?

ConcepTest 21.7aConcepTest 21.7a Circuits ICircuits I

1) circuit 1circuit 1

2) circuit 2circuit 2

3) both the sameboth the same

4) it depends on it depends on RR

The lightbulbs in the circuit below The lightbulbs in the circuit below are identical with the same are identical with the same resistance resistance RR. Which circuit . Which circuit produces more light? (brightness produces more light? (brightness power) power)

ConcepTest 21.7aConcepTest 21.7a Circuits ICircuits I

1) circuit 1circuit 1

2) circuit 2circuit 2

3) both the sameboth the same

4) it depends on it depends on RR

The lightbulbs in the circuit below The lightbulbs in the circuit below are identical with the same are identical with the same resistance resistance RR. Which circuit . Which circuit produces more light? (brightness produces more light? (brightness power) power)

In #1, the bulbs are in parallelparallel, lowering the total resistancelowering the total resistance of the circuit. Thus, circuit #1 will#1 will draw draw a higher currenta higher current, which leads to more light, because P = I VP = I V.

ConcepTest 21.7bConcepTest 21.7b Circuits IICircuits II

1) twice as muchtwice as much

2) the samethe same

3) 1/2 as much1/2 as much

4) 1/4 as much 1/4 as much

5) 4 times as much 4 times as much

10 V10 V

A

B C

The three lightbulbs in the circuit all have The three lightbulbs in the circuit all have the the same resistance ofsame resistance of 1 1 By how By how much is the much is the brightness of bulb B brightness of bulb B greater greater or smaller than the or smaller than the brightness of bulb Abrightness of bulb A? ? (brightness (brightness power) power)

ConcepTest 21.7bConcepTest 21.7b Circuits IICircuits II

1) twice as muchtwice as much

2) the samethe same

3) 1/2 as much1/2 as much

4) 1/4 as much 1/4 as much

5) 4 times as much 4 times as much

10 V10 V

A

B CWe can use P = V2/R to compare the power:

PPAA = ( = (VA)2/RA = (10 V) 2/1 = 100 W= 100 W

PPBB = ( = (VB)2/RB = (5 V) 2/1 = 25 W= 25 W

The three lightbulbs in the circuit all have The three lightbulbs in the circuit all have the the same resistance ofsame resistance of 1 1 By how By how much is the much is the brightness of bulb B brightness of bulb B greater greater or smaller than the or smaller than the brightness of bulb Abrightness of bulb A? ? (brightness (brightness power) power)

Follow-up:Follow-up: What is the total current in the circuit? What is the total current in the circuit?

ConcepTest 21.8aConcepTest 21.8a More Circuits IMore Circuits I

1) increaseincrease

2) decreasedecrease

3) stay the samestay the same

What happens to the voltage What happens to the voltage

across the resistor across the resistor RR11 when the when the

switch is closed? The voltage will:switch is closed? The voltage will:

V

R1

R3

R2

S

ConcepTest 21.8aConcepTest 21.8a More Circuits IMore Circuits I

1) increaseincrease

2) decreasedecrease

3) stay the samestay the same

What happens to the voltage What happens to the voltage

across the resistor across the resistor RR11 when the when the

switch is closed? The voltage will:switch is closed? The voltage will:

With the switch closed, the addition of R2 to R3 decreases the equivalent decreases the equivalent

resistanceresistance, so the current from the current from the battery increasesbattery increases. This will cause an

increase in the voltage across increase in the voltage across RR11 .

V

R1

R3

R2

S

Follow-up:Follow-up: What happens to the current through R3??

ConcepTest 21.8bConcepTest 21.8b More Circuits IIMore Circuits II

1) increasesincreases

2) decreasesdecreases

3) stays the samestays the same

V

R1

R3 R4

R2

S

What happens to the voltage What happens to the voltage across the across the resistor resistor RR44 when the when the

switch is closed?switch is closed?

V

R1

R3 R4

R2

S

A B

C

We just saw that closing the switch causes an increase in the voltage increase in the voltage across across RR11 (which is VVABAB). The voltage of the battery is constantconstant, so if VVABAB increases increases, then VVBCBC must must

decreasedecrease!

What happens to the voltage What happens to the voltage across the across the resistor resistor RR44 when the when the

switch is closed?switch is closed?

1) increasesincreases

2) decreasesdecreases

3) stays the samestays the same

ConcepTest 21.8bConcepTest 21.8b More Circuits IIMore Circuits II

Follow-up:Follow-up: What happens to the current through R4??

ConcepTest 21.9ConcepTest 21.9 Even More Circuitsircuits

Which resistor has the Which resistor has the greatest current going greatest current going through it? Assume that all through it? Assume that all the resistors are equal.the resistors are equal.

V

R1

R2

R3

R5

R4

1) R1

2) both R1 and and R2 equally

3) R3 and and R4

4) R5

5) all the same

The same current must flow through left and right combinations of resistors. On the LEFT, the current splits equally, so II11 = = II22. On the RIGHT, more current will go through RR55 than RR33 + + RR44 since the branch containing branch containing RR55 has less resistance has less resistance.

ConcepTest 21.9ConcepTest 21.9 Even More Circuitsircuits1) R1

2) both R1 and and R2 equally

3) R3 and and R4

4) R5

5) all the same

Which resistor has the Which resistor has the greatest current going greatest current going through it? Assume that all through it? Assume that all the resistors are equal.the resistors are equal.

V

R1

R2

R3

R5

R4

Follow-up:Follow-up: Which one has the smallest voltage drop??

ConcepTest 21.10ConcepTest 21.10 Dimmer Dimmer

When you rotate the knob of a When you rotate the knob of a

light dimmer, what is being light dimmer, what is being

changed in the electric circuit?changed in the electric circuit?

1) the power

2) the current

3) the voltage

4) both (1) and (2)

5) both (2) and (3)

The voltage is provided at 120 V from the outside. The light dimmer increases the increases the resistanceresistance and therefore decreases the decreases the currentcurrent that flows through the lightbulb.

ConcepTest 21.10ConcepTest 21.10 Dimmer Dimmer

When you rotate the knob of a When you rotate the knob of a

light dimmer, what is being light dimmer, what is being

changed in the electric circuit?changed in the electric circuit?

1) the power

2) the current

3) the voltage

4) both (1) and (2)

5) both (2) and (3)

Follow-up:Follow-up: Why does the voltage not change? Why does the voltage not change?

ConcepTest 21.11aConcepTest 21.11a LightbulbsLightbulbs

Two lightbulbs operate at 120 V, but one Two lightbulbs operate at 120 V, but one has a power rating of has a power rating of 25 W25 W while the while the other has a power rating of other has a power rating of 100 W100 W. . Which one has the greater resistance? Which one has the greater resistance?

1) the 25 W bulb

2) the 100 W bulb

3) both have the same

4) this has nothing to do with resistance

Since P = VP = V22 / R / R ,, the bulb with the lower lower power ratingpower rating has to have the higher higher resistanceresistance.

ConcepTest 21.11aConcepTest 21.11a LightbulbsLightbulbs

Two lightbulbs operate at 120 V, but one Two lightbulbs operate at 120 V, but one has a power rating of has a power rating of 25 W25 W while the while the other has a power rating of other has a power rating of 100 W100 W. . Which one has the greater resistance? Which one has the greater resistance?

1) the 25 W bulb

2) the 100 W bulb

3) both have the same

4) this has nothing to do with resistance

Follow-up:Follow-up: Which one carries the greater current? Which one carries the greater current?

ConcepTest 21.11bConcepTest 21.11b Space Heaters ISpace Heaters I

Two space heaters in your living Two space heaters in your living room are operated at 120 V. room are operated at 120 V. Heater 1 has Heater 1 has twicetwice the resistance the resistance of heater 2. Which one will give of heater 2. Which one will give off more heat?off more heat?

1) heater 1

2) heater 2

3) both equally

Using P = VP = V22 / R, / R, the heater with the smaller resistancesmaller resistance

will have the larger powerlarger power output. Thus, heater 2 will

give off more heat.

ConcepTest 21.11bConcepTest 21.11b Space Heaters ISpace Heaters I

Two space heaters in your living Two space heaters in your living room are operated at 120 V. room are operated at 120 V. Heater 1 has Heater 1 has twicetwice the resistance the resistance of heater 2. Which one will give of heater 2. Which one will give off more heat?off more heat?

1) heater 1

2) heater 2

3) both equally

Follow-up:Follow-up: Which one carries the greater current? Which one carries the greater current?

ConcepTest 21.12ConcepTest 21.12 Junction RuleJunction Rule

1) 2 A2) 3 A3) 5 A4) 6 A5) 10 A

5 A

8 A

2 A

P

What is the current in branch P?What is the current in branch P?

The current entering the junction in redred is 8 A, so the current leaving must also be 8 A. One One exiting branch has 2 Aexiting branch has 2 A, so the other branch (at P) must have 6 other branch (at P) must have 6 AA.

5 A

8 A

2 A

P

junction 6 A

SS

1) 2 A2) 3 A3) 5 A4) 6 A5) 10 A

What is the current in branch P?What is the current in branch P?

ConcepTest 21.12ConcepTest 21.12 Junction RuleJunction Rule

ConcepTest 21.13ConcepTest 21.13 Kirchhoff’s RulesKirchhoff’s RulesThe lightbulbs in the The lightbulbs in the circuit are circuit are identicalidentical. . When the switch is When the switch is closed, what happens?closed, what happens?

1) both bulbs go out2) intensity of both bulbs increases3) intensity of both bulbs decreases4) A gets brighter and B gets dimmer5) nothing changes

When the switch is open, the point the point between the bulbs is at 12 Vbetween the bulbs is at 12 V. But so But so is the point between the batteriesis the point between the batteries. If there is no potential difference, then no current will flow once the switch is closed!! Thus, nothing changes.

The lightbulbs in the The lightbulbs in the circuit are circuit are identicalidentical. . When the switch is When the switch is closed, what happens?closed, what happens?

1) both bulbs go out2) intensity of both bulbs increases3) intensity of both bulbs decreases4) A gets brighter and B gets dimmer5) nothing changes

ConcepTest 21.13ConcepTest 21.13 Kirchhoff’s RulesKirchhoff’s Rules

24 VFollow-up:Follow-up: What happens if the bottom battery is replaced by a 24 V battery?

ConcepTest 21.14ConcepTest 21.14 Wheatstone BridgeWheatstone Bridge1) 1) II2) 2) I/2I/23) 3) I/3I/34) 4) I/4I/45) zero5) zero

An ammeter A is connected An ammeter A is connected between points between points aa and and bb in the in the circuit below, in which the four circuit below, in which the four resistors are resistors are identicalidentical. The current . The current through the ammeter is:through the ammeter is:

II

VV

aa

bb

Since all resistors are identicalresistors are identical, the voltage drops are the samevoltage drops are the same across the upper branch and the lower branch. Thus, the potentialspotentials at points aa and bb are also the samesame. Therefore, no current flows.

ConcepTest 21.14ConcepTest 21.14 Wheatstone BridgeWheatstone Bridge1) 1) II2) 2) I/2I/23) 3) I/3I/34) 4) I/4I/45) zero5) zero

An ammeter A is connected An ammeter A is connected between points between points aa and and bb in the in the circuit below, in which the four circuit below, in which the four resistors are resistors are identicalidentical. The current . The current through the ammeter is:through the ammeter is:

II

VV

aa

bb

ConcepTest 21.15ConcepTest 21.15 More Kirchhoff’s RulesKirchhoff’s Rules

2 V

2

2 V 6 V

4 V

3 1

1

I1 I3

I2

Which of the equations is valid Which of the equations is valid for the circuit below? for the circuit below?

1) 1) 2 – I2 – I11 – 2I – 2I22 = 0 = 0

2) 2) 2 – 2I2 – 2I11 – 2I – 2I2 2 – 4I– 4I3 3 = 0= 0

3) 3) 2 – I2 – I11 – 4 – 2I – 4 – 2I2 2 = 0= 0

4) 4) II33 – 4 – 2I – 4 – 2I2 2 + 6 + 6 = 0= 0

5) 5) 2 – I2 – I11 – 3I – 3I3 3 – 6– 6 = 0= 0

ConcepTest 21.15ConcepTest 21.15 More Kirchhoff’s RulesKirchhoff’s Rules

2 V

2

2 V 6 V

4 V

3 1

1

I1 I3

I2

Eqn. 3 is valid for the left loopEqn. 3 is valid for the left loop: The left battery gives +2V, then there is a drop through a 1 resistor with current I1 flowing. Then we go through the middle battery (but from + to – !), which gives –4V. Finally, there is a drop through a 2 resistor with current I2.

Which of the equations is valid Which of the equations is valid for the circuit below? for the circuit below?

1) 1) 2 – I2 – I11 – 2I – 2I22 = 0 = 0

2) 2) 2 – 2I2 – 2I11 – 2I – 2I2 2 – 4I– 4I3 3 = 0= 0

3) 3) 2 – I2 – I11 – 4 – 2I – 4 – 2I2 2 = 0= 0

4) 4) II33 – 4 – 2I – 4 – 2I2 2 + 6 + 6 = 0= 0

5) 5) 2 – I2 – I11 – 3I – 3I3 3 – 6– 6 = 0= 0

ConcepTest 21.16aConcepTest 21.16a Capacitors ICapacitors I

o

o

C CC

Ceq

1) 1) CCeqeq = 3/2 = 3/2 CC

2) 2) CCeqeq = 2/3 = 2/3 CC

3) 3) CCeqeq = 3 = 3 CC

4) 4) CCeqeq = 1/3 = 1/3 CC

5) 5) CCeqeq = 1/2 = 1/2 CC

What is the equivalent capacitance, What is the equivalent capacitance,

Ceq , of the combination below? , of the combination below?

The 2 equal capacitors in seriesseries add up as inversesinverses, giving 1/2 1/2 CC. These are parallelparallel to the first one, which add up directlydirectly. Thus, the total equivalent capacitance is 3/2 3/2 CC.

ConcepTest 21.16aConcepTest 21.16a Capacitors ICapacitors I

o

o

C CC

Ceq

1) 1) CCeqeq = 3/2 = 3/2 CC

2) 2) CCeqeq = 2/3 = 2/3 CC

3) 3) CCeqeq = 3 = 3 CC

4) 4) CCeqeq = 1/3 = 1/3 CC

5) 5) CCeqeq = 1/2 = 1/2 CC

What is the equivalent capacitance, What is the equivalent capacitance,

Ceq , of the combination below? , of the combination below?

ConcepTest 21.16bConcepTest 21.16b Capacitors IICapacitors II1) 1) VV11 == VV22

2) 2) VV11 >> VV22

3) 3) VV11 << VV22

4) all voltages are zero4) all voltages are zero

CC11 = 1.0 = 1.0 FF CC33 = 1.0 = 1.0 FF

CC22 = 1.0 = 1.0 FF

10 V10 V

How does the voltage How does the voltage VV11 across across

the first capacitor (the first capacitor (CC11) compare to ) compare to

the voltage the voltage VV22 across the second across the second

capacitor (capacitor (CC22)?)?

ConcepTest 21.16bConcepTest 21.16b Capacitors IICapacitors II1) 1) VV11 == VV22

2) 2) VV11 >> VV22

3) 3) VV11 << VV22

4) all voltages are zero4) all voltages are zero

CC11 = 1.0 = 1.0 FF CC33 = 1.0 = 1.0 FF

CC22 = 1.0 = 1.0 FF

10 V10 V

The voltage across C1 is 10 V. The combined capacitors C2+C3 are parallel to C1. The voltage across C2+C3 is also 10 V. Since C2 and C3 are in series, their voltages add. Thus the voltage across C2 and C3 each has to be 5 V, which is less than V1.

How does the voltage How does the voltage VV11 across across

the first capacitor (the first capacitor (CC11) compare to ) compare to

the voltage the voltage VV22 across the second across the second

capacitor (capacitor (CC22)?)?

Follow-up:Follow-up: What is the current in this circuit??

ConcepTest 21.16cConcepTest 21.16c Capacitors IIICapacitors III

CC11 = 1.0 = 1.0 FF CC33 = 1.0 = 1.0 FF

CC22 = 1.0 = 1.0 FF

10 V10 V

1) 1) QQ11 == QQ22

2) 2) QQ11 >> QQ22

3) 3) QQ11 << QQ22

4) all charges are zero4) all charges are zero

How does the charge How does the charge QQ11 on the first on the first

capacitor (capacitor (CC11) compare to the charge ) compare to the charge

QQ22 on the second capacitor ( on the second capacitor (CC22)?)?

ConcepTest 21.16cConcepTest 21.16c Capacitors IIICapacitors III

CC11 = 1.0 = 1.0 FF CC33 = 1.0 = 1.0 FF

CC22 = 1.0 = 1.0 FF

10 V10 V

We already know that the voltage across C1 is 10 V and the voltage across both C2 and C3 is 5 V each. Since

QQ = = CVCV and C is the samesame for all the capacitors, then since since VV11 > V > V22 therefore QQ11 > Q > Q22.

1) 1) QQ11 == QQ22

2) 2) QQ11 >> QQ22

3) 3) QQ11 << QQ22

4) all charges are zero4) all charges are zero

How does the charge How does the charge QQ11 on the first on the first

capacitor (capacitor (CC11) compare to the charge ) compare to the charge

QQ22 on the second capacitor ( on the second capacitor (CC22)?)?