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Unformatted text preview: Problems: Week 6 6~1. What is EMF (electromotive force)? [Hint: It is not a force] Q2 0 6—2. In order to place a charge Q on a capacitor C0 the battery must do joules of work. Where does all this energy go? Why? 6—3. Use the result of 62 for a parallel plate capacitor With air or vacuum between the plates to show that III)3 of an E ~ﬁeld stores 1£0132 joules of energy. 2 64. A current of lamp exists in a resistor for 4 min. How many (a) cculombs and (b)
electrons pass through any crosssection? 6—5. 66. 6—7. 6—8. If the resistor of problem 6~4 is a cylinder of radius 0.001111, what is the current density? TWO conductors A and B are made of the same material and have the same length.
However, A is solid and has a diameter of 1m, B is hollow with an outer diameter of
2mm and an inner diameter of 1mm. Calculate the resistance ratio R A /RB . A wire with resistance 69 is drawn out so that its length is tripled. If neither density nor
the resistivity change, what will be the resistance of the longer wire? _ \
Using the result of 36, if there is a current of lamp in a Cu Wire of diameter 1mm, what
will be the drift speed (VD) of the electrons? [e[ = 1.6 ><10”19 C ]? Why? 6—9. If in 6—8 the diameter is doubled by what factor will VD change? Why? > . 6~10. When the resistance(R) is independent of the current one writes the socalled Ohm’s Law
V=IR —— (l)
1
034
where Z is the length and a the electrical conductivity. Show that Eq. (1) implies the
fundamental relationship 1 = 0 E where g is the ﬁeld driving the current. Now I = i 14, where i is the current density and A the area of the conductor, R = 611. The conductivity of copper is 5.9 x 107(0. — m)‘1 . Use the result of problem 3—6 (for n) to
estimate the time 7» between collisions in Cu if i '
2
ne 1 0":
m e=1.0><10”'9C; m=9><10‘3'kg 6—12. At room temperature the resistivities of Copper and Iron are 1.7 x1039 — m anle x10“8£2 — m. A composite wire is made up of 1m each of Cu and Fe connected as
shown. The diameters are 1mm. (i) What is the total resistance? (ii) What is the current _
if there is a voltage difference of 10V between A and B? (iii) What is the potential at C? [swan WWW 613. How much thermal energy per hour is generated by the current in problem 6—12? Why? 6—14. In the circuit shown, what is the equivalent resistance across AB? Next, close the switch
and calculate (i) the currents in the resistors and (ii) the potential drop across each
resistor. 615. In the circuit shown "r" is the internal resistance of the battery. Calculate the power
dissipated in the load R and show that the power becomes very small when R << r or
R >> r . 616. In problem 6—12 if the wires are connected as shown here, now what is the resistance AB
and the current in each if VAB = 10V ? ...
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 Fall '11
 Bhagat
 Physics

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