PHYS 251 TEST #4 06/30/06 Dr. Holmes NAME

DO ALL EIGHT PROBLEMS. THE WORTH OF EACH PROBLEM IS MARKED NEXT TO THE PROBLEM. SHOW YOUR WORK FOR PARTIAL CREDIT. ALL ANSWERS SHOULD BE IN MKS UNITS UNLESS OTHERWISE INDICATED.

Choices for answers to questions (2-c,d,e), (4-d,e), (5-d), (7-h,i,j):
a. decrease by a factor of 1/4
b. decrease by a factor of 1/2
c. decrease by a factor of 1/Ö2
d. decrease but not by one of the "nice factors
e. stay the same
f. increase by a factor of Ö2
g. increase by a factor of 2
h. increase by a factor of 4
i. increase but not by one of the "nice" factors
k. can't tell from information given

1) Name and write down Maxwell's four equations.

a)

b)

c)

d)

2) Consider the situation depicted in the figure to the right:

The conducting bar is moving at a speed of 11.3 m/s (v) to the right across conducting rails that are 20 cm apart (w). The present distance of the bar from the connected end of the rails is 40 cm (l). The strength of the external magnetic field is a constant and uniform .21 T directed up (B).

a) What is the voltage induced in the circuit formed by the bar and the rails?

0.475 V.

b) If the circuit has a resistance of 6 W , what will the induced current be in the circuit due to this induced voltage?

.079 A.

c) If the speed of the bar is twice as fast, how will the induced current in the circuit change? (choice a-k above)?

g (increase by factor of 2).

d) If the magnetic field is cut doubled, how will the induced current in the circuit change (choice a-k above)?

g (increase by factor of 2)

e) If the distance of the bar from the connected end is twice as long, how will the induced current in the circuit change (choice a-k above)?

e (same)

3) Clearly draw in the direction of the induced current in each of the three diagrams, or write NONE if there is no induced current.

a) the South magnetic pole is moving away from the solenoid of circuit A.

b) the loop is rotating so that the left is moving into the page and the right side is moving out of the page.

c) consider the induced current in the circuit labeled B due to the switch being closed in the circuit labeled A.

4) DESIGN an electric generator that produces 12,000 volts rms at 60 Hz that uses a coil that rotates in an external magnetic field:

a) Draw a picture:

b) Specify the values for all parameters:

c) What is the amplitude of the sine wave voltage produced?

16,970 Volts.

d) If the number of turns of the coil is situated is doubled, will the rms voltage: (choose one from list at top of page 1)

g (increase by factor of 2)

e) If the frequency of rotation is doubled (from 60 Hz to 120 Hz), will the rms voltage: (choose one from list at top of page 1)

g (increase by factor of 2)

5) Consider an inductor of 0.9 H.

a) How much current would have to flow through the inductor for it to store 1 Joule of energy?

1.49 Amps.

b) If the current was raised from zero to this value at a constant rate over 5 seconds, what was the voltage across the inductor during those five seconds?

0.268 Volts.

c) If the current oscillates as a sine function with the above current as its amplitude (AC current) and with a frequency of 60 Hz, what will the amplitude of the voltage across the inductor be?

505 Volts.

d) If the frequency of the current is doubled (but the amplitude of the current remains unchanged), will the amplitude of the voltage across the inductor: (choose one from list at top of page 1)

g (increase by factor of 2)

6) a) DESIGN a series LRC circuit that has a natural resonance frequency of 680 KHz?

(many answers possible)

b) Give a mechanical analogue of this circuit, that is, give the mechanical analogue of:

Electrical quantity --Mechanical quantity analogue (symbol plus descriptive word)

L, inductance -- m, mass

R, resistance -- b, air resistance coefficient

C, capacitance -- 1/k where k = spring constant

I, current -- v, velocity

Q, charge -- x, position

t, time -- t, time

7) Consider a series LRC circuit with an oscillating voltage source of 110 volts (rms) at 60 Hz. The resistance is 65 W , the capacitance is 2 mF, and the inductance is 0.9 H.

a) What is the capacitive reactance (X_C)?

1,326 W .

b) What is the inductive reactance (X_L)?

339 W

c) What is the impedance (Z) of the circuit?

989 W .

d) What is the rms current in the circuit?

.111 Amps (rms).

e) What is the rms voltage across the inductor (V_L-rms)?

37.7 Volts (rms).

f) Does the V_AC-rms = V_L-rms + V_C-rms + V_R-rms ?

No.

g) Does the V_AC(t) = V_L(t) + V_C(t) + V_R(t) ?

Yes.

h) If the frequency of the voltage source is doubled to 120 Hz, how will the rms current in the circuit change (use one of the choices from the top of page 1):

i (increase but not by one of the "nice" factors)

i) If the amplitude of the voltage from the source is doubled, how will the current change (use one of the choices from the top of page 1):

g (increase by factor of 2)

j) If the capacitance is doubled, how will the current change (use one of the choices from the top of page 1):

i (increase but not by one of the "nice" factors).

8. Consider a solenoid with 3,000 turns wrapped around a cylinder of radius 6 cm and length 20 cm. The inductor is part of a DC circuit that contains a 12 volt battery and 2 ohms of resistance. An iron bar is inserted into the cylinder. For each of the following quantities, answer Y if the insertion of the iron changes the quantity, D if it changes the qunatity only during the insertion, or answer N if it doesn't: affect the quantity at all:

a) L_inductance ? Y

b) V_inductor ? D

c) B_inside ? Y

d) H_inside ? D

e) M_inside ? Y

e) Energy stored in inductor? Y

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