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Physics 226

Problem Set #6

.

1) Analyze the circuit below using a V-I-R chart.

2) Analyze the circuit below using a V-I-R chart.

3) Analyze the circuit below using a V-I-R chart.

4) In the circuit below, the current through R4 is 0.5 A. Find the current
through (a) R5 and (b) R2.

ANSWERS:
1) Req=4.6 Ω 5) 2.22 W 9) I1 = 3.5

A

2) Req=5.13 Ω 6) 0.429 A I2 = 1.0 A
3) Req=15 Ω 7) 0.12 Ω

I3

= 2.5 A
4) a) 0.75 A, b) 2.11 A 8) 0.38 A

5) Determine the power dissipated in R4 in the circuit below.

6)Find the current through the 12 Ω resistor in the circuit below.

7) A 1.4 Ω resistor is connected across a 9 V battery. The voltage
between the terminals of the battery is observed to be 8.3 V. Find the
internal resistance of the battery.

8) From the information given in the circuit below, (a) determine the
current in the circuit, and (b) state which point, A or B, is at a higher
potential.

9)Calculate the unknown currents I1,
I2, and I3 for the circuit below.

R1

Values

R1 = 20 Ω
R2 = 3.0 Ω
R3 = 4.0 Ω
R4 = 9.0 Ω
R5 = 8.0 Ω
R6 = 6.0 Ω

R2

R3

R4

R5

R6

20 V

Values
R1 = 3.0 Ω

R2 = 10.0 Ω
R3 = 5.0 Ω
R4 = 4.0 Ω
R5 = 3.0 Ω

R1

R2

R3

R4

R5

40 V

Values
R1 = 6.0 Ω
R2 = 6.0 Ω
R3 = 2.

4 Ω

R4 = 6.0 Ω
R5 = 9.0 Ω
R6 = 6.0 Ω

15 V

R1
R2
R3
R4

R5 R6

Values
R1 = 18.0 Ω
R2 = 9.0 Ω

R3 = 16.0 Ω
R4 = 8.0 Ω

R5 = 20.0 Ω R1

R2
R5
R4
R3
R1

R2 R3

R4 R5

12 V

Values
R1 = 4.0 Ω
R2 = 2.0 Ω
R3 = 1.0 Ω
R4 = 5.0 Ω
R5 = 1.0 Ω

R2
R1
R3
R4

R5
R7

R6
18 V

Values
R1 = 3.0 Ω
R2 = 3.0 Ω
R3 = 6.0 Ω
R4 = 6.0 Ω
R5 = 4.0 Ω
R6 = 12.0 Ω
R7 = 2.0 Ω

8 Ω

5 Ω

1

2 Ω

27 Ω

10 V

30 V

A

B

24 V

12 V
2 Ω
4 Ω

3 Ω

5 Ω

1 Ω

I1

I2

I3

Values
Values
Values
Values
Values
Values

Physics 226

Problem Set #7

1) Consider a series RC circuit at the left where C =

6 µ F, R = 2 MΩ, and ε = 20 V. You close the
switch at t = 0. Find (a) the time constant for the
circuit, (b) the half-life of the circuit, (c) the current
at t = 0, (d) the voltage across the capacitor at t = 0,
and (e) the voltage across the resistor after a very
long time

.

2) Given the circuit at the right in which
the following values are used: R1 = 5
kΩ, R2 = 10 kΩ, C = 8 µ F, and ε = 20
V. You close the switch at t = 0. Find
(a) the current through R2 at t=0, and (b)
the voltage across R1 after a long time.

3) Given the circuit at the right in which the
following values are used: R1 = 20 kΩ, R2 =
12 kΩ, C = 10 µ F, and ε = 25 V. You
close the switch at t = 0. Find (a) the
current in R1 and R2 at t=0, (b) the voltage
across R1 after a long time. (Careful with
this one.)

.

4) Using the drawings below: (a) Find the direction of the force on a
proton moving through the magnetic field. (b) Repeat with an electron.

5) An alpha particle has a charge of +2e and a mass of 6.64 x 10-27 kg. It
is accelerated from rest through a potential difference of 1.2 x 106 V and then
enters a uniform magnetic field whose strength is 2.2 T. The alpha particle
moves perpendicular to the field. Calculate (a) the speed of the alpha
particle, (b) the magnitude of the magnetic force exerted on it, and (c) the
radius of its circular path.

6) A 50 g horizontal copper rod has a length of 1.0 m. Calculate the
minimum current in the rod so that it will float in a horizontal magnetic field
of 2.0 T.

7) A 0.5 m length of wire is bent to
form a single square loop. The loop has
12 A of current running through it. The
loop is placed in a magnetic field of
0.12 T as shown at the right (side view
of loop). What is the maximum torque
that the loop can experience?

8) Two very long wires, as shown in the
diagram at the right, each carry currents of
8.0 A, however, they flow in opposite
directions. The distance between the two
wires is 0.12 m. Calculate the net magnetic
field at point A, which is 0.03 m to the left
of the left wire, and at point

B

, which is
halfway between the two wires.

9) A mass spectrometer is shown below. A single charged ion is shot through
the velocity selector into the rectangular deflection chamber. The electric
field between the plates of the velocity selector is 950 V/m. The magnetic
field in the velocity selector and the deflection chamber is 0.93 T. Calculate
the radius of the path of the singly charged ion that has a mass 2.18 x 10 -26

kg.

8)

9)

10) An electron moves at a speed of 1.0 x 104 m/s in a circular
path of radius 2 cm inside a solenoid. The magnetic field of the solenoid is
perpendicular to the plane of the electron’s path. Calculate (a) the
strength of the magnetic field inside the solenoid and (b) the current in the
solenoid if it has 25 turns per centimeter.

ANSWERS:
1) a) 12 s, b) 8.32 s, 5) a) 1.08 x 107 m/s 9) 1.49 x 10-4 m

c) 1 x 10-5 A b) 7.6 x 10-12 N 10) a) 2.8 x 10-6 T
2) a) 2 mA, b) 20 V c) 1.02 x 10-1 m b) 0.89 mA

3) a) I1=1.25 mA, I2=0 6) 0.245 A
b) 15.6 V 7) 0.023 Nm

4) a) P-West, E-East 8) a) 4.3 x 10-5 T
b) 5.3 x 10-5 T

ε

C

R

R1 R2

C
ε
ε

R1

R2 C

v v
v v

B

B

B B

(a) (b) (c) (d)

B

F

F

A B

Electric
Field

Velocity Selector

B