Physics 2B Spring 2010: Quiz 3 Version A 1

05.07.10

Closed book. No work needs to be shown for multiple-choice questions.

1. The time constant for one RC circuit is known to be 1.2 seconds (we will call this the first RC circuit). A second RC circuit is known to have a time constant of 3.6 seconds. Initially, the two capacitors are fully charged and both circuits have open switches. The circuits are then closed and the capacitors are discharged until they have one-fourth of their original charge. Which of the following is true?

a) The first RC circuit takes one-third as long to complete this process as the second. b) The first RC circuit takes three times as long to complete this process as the second. c) The first RC circuit takes one-fourth as long to complete this process as the second. d) The first RC circuit takes four times as long to complete this process as the second. e) The first RC circuit takes 2.4 seconds longer to compete this process than the second.

2. The figure shows a resistor made from a truncated cone of material with resistivity ρ. By

integrating by slices, please find the resistance between the two flat surfaces.

a. 2ρh/(r1+r2) b. ρπr1r2/h c. ρh/(πr1r2) d. ρπh/(r1r2)

e. 2ρh/(πr1r2)

3. One bulb dissipating 100.0 W is connected in parallel to another bulb that is dissipating 150.0 W. The pair is then connected to a 10.0 V battery (all three circuit elements are in parallel). After 2.0 hours, which of the following is true?

a) The 100.0 W bulb has used 200 kWh. b) The 100.0 W bulb has used 100 kWh. c) The 100.0 W bulb has used 0.50 kWh. d) The 100.0 W bulb has used 0.20 kWh. e) The 100.0 W bulb has used 0.10 kWh.

Physics 2B Spring 2010: Quiz 3 Version A 2

05.07.10

4. For the circuit below the ε1 = 14V, ε2 = 3V and ε3 = 20V. What is the value of the current flowing through R2?

a. 1.0 mA. b. 1.5 mA. c. 2.0 mA. d. 3.0 mA. e. 4.0 mA.

5. If the currents in resistors R1 and R2 are 2A in both of them, the value of resistors R1 and R2 are, respectively,

a. 6 Ω and 8 Ω. b. 2 Ω and 2 Ω. c. 6 Ω and 4 Ω. d. 1 Ω and 6 Ω. e. 8 Ω and 6 Ω.

Physics 2B Spring 2010: Quiz 3 Version A 3

05.07.10

6. The equivalent resistor connected to the 12V battery is: a. 20 Ω. b. 52 Ω. c. 60 Ω. d. 40 Ω. e. 48 Ω.

7. A series RC circuit has a time constant of 2.0 s. The battery has a voltage of 50 V and the maximum current just after closing the switch is 1A. The capacitor is initially uncharged. What is the charge on the capacitor 4.0 s after the switch is closed?

a. 1.73 C b. 2.64 C c. 0.86 C d. 1.16 C e. 0.17 C

50 V

R

C

8. What is the equivalent resistance for these 3.00 Ω resistors between points a and b?

a. 1.33 Ω b. 2.25 Ω c. 3.00 Ω d. 7.50 Ω e. 0.75 Ω

3 !

3 !

3 ! 3 !

a b

Physics 2B Spring 2010: Quiz 3 Version A 4

05.07.10

Recall that

!

F = keq

1 q

2

r2

; ke = 8.99

!

"109

!

N "m2

C2

; e = 1.60

!

"10#19C; εο = 8.85!10 "12

!

C2

N "m2

;

!

me = 9.11

!

"10#31 kg;

!

mp = 1.673

!

"10#27 kg;

!

mn = 1.675

!

"10#27 kg;

!

1 eV =1.602 "10#19

J;

!

1 kWh = 3.60 "106J ;

!

r F = qo

r E ;

!

E = keq

r2

;

!

"E

= EAcos# ;

!

"E =Qinside

#0

;

!

PEelec,point = keqq0

r;

!

Vpoint charge = ke

q

r;

!

"PEelec = q0"V ;

!

C =Q

"V;

!

Cparllel plate = "0

A

d;

!

Cdielectric

="#0

A

d;

!

1

Cseries eq

=1

C1

+1

C2

+1

C3

+K;

!

Cparallel eq =C1+C

2+C

3+K;

!

Energycapacitor =1

2Q "V( ) =

1

2C "V( )

2

=Q2

2C;

!

I ="Q

"t;

!

R ="V

I= #

L

A;

!

" = "o1+# T $T

o( )[ ];

!

R = Ro1+" T #T

o( )[ ];

!

Power = I "V( ) = I2R ="V( )

2

R;

!

"Silver

=1.59 #10$8%&m ;

!

"Copper =1.7 #10$8%&m

!

Iin

= Iout

;

!

1

Rparallel eq

=1

R1

+1

R2

+1

R3

+K;

!

Rseries eq = R1+ R

2+ R

3+K;

!

"Vloop# = 0;

!

" = RC ;

!

qcharge =Qfinal 1" e– t /RC( );

!

qdischarge =Q0e– t /RC ;

!

Acircle

= "r2 ;

!

Acyl . side = 2"rh ;

!

Asphere = 4"r2 ;

!

g = 9.80 m/s2 ;

!

x ="b ± b

2" 4ac

2a;

!

100 cm =1 m;

!

1 µF =1.0 "10#6

F ;

!

1 MW =1.0 "106W ;

!

1,000 W =1 kW ; 60 s = 1 min;

!

60 min =1 hr;

!

2.54 cm =1 in;

!

12 in =1 ft ;

!

5,280 ft =1 mi ;

!

1,609 m =1 mi;

!

0.3048 m =1 ft .