Download PHYS 196 Class Problem 1

PHYS 196 Home Work 7
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1. The life time of a 12.0V battery is 1,000 Ampere-hours. What is the total amount of energy (in kWh)
and electric charge it can deliver?
2. Find the drift speed of electrons in a 10-gauge copper wire carrying a 20A current. (area of wire
=5.261mm2, density of copper = 8.93g/cc, atomic weight = 63.5g/mole, one conduction electron is
donated by each atom.)
3. In a proton accelerator, the energy of proton is 20MeV, the diameter of the beam is 2.0mm, and the
beam current is 1.0mA. Find the current density and the particle density in the beam.
4. A 5.0nC point charge travels in a circle of radius 1.0cm. What is its speed so that the current it generates
is 1.0mA?
5. A thin non-conducting ring that has a radius a and a linear charge density  rotates with angular speed
 about an axis through its center and perpendicular to the plane of the ring. Find the current of the
ring.
6. (a) What is the length of a 16-gauge (area=1.309mm2) silver wire at 20C so that its electrical resistance
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is 10.0? (resistivity of silver at 20C
(b) What is the electrical resistance of a silver ring of diameter 1.2cm if its 10mm2 cross-section area can
be considered quite small in comparison with its diameter?
7. While remodeling your garage, you need to temporarily splice, end to end, an 80-m long copper wire
that is 1.00mm in diameter with a 49-m long aluminum wire that has the same diameter. When the wire
carries the maximum current of 2.00A, find (a) the potential drop across each wire, and (b) the electric
field in each wire. (resistivity of copper = 1.710-8-m, of aluminum = 2.810-8-m)
8. Consider a wire of length L in the shape of a truncated cone. The radius of the wire varies with distance
x from the narrow end according to r  a  b  a/Lx , where 0  x  L . Derive an expression for the
resistance of this wire in terms of its length L , radius a , radius b , and resistivity  .
9. A battery has an
emf of 12 V. How much work does it do in 5.0s if it delivers a current of 3.0 A?
10. What is the current and the power dissipated in a 50 resistor
when a voltage of 120 V is applied across
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its terminals?
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11. (a) A hair dryer has a power rating of 25W (when used with the standard120 V electrical outlet). What
is its resistance? What is the current it draws when in use?
(b) An electric heater is rated at 1,000W. Without doing any calculation, answer the following questions:
(1) Does it have higher or lower electrical resistance than the hair dryer? (2) Does it draw more or less
current than the hair dryer?
12. Draw a circuit diagram of three resistors with resistance 5, 10, and 20 in series. Find the equivalent
resistance. A potential difference of 70V is applied across the terminals of the combination. For each
resistor, calculate (a) the current through it, (b) the potential difference across it, and (c) the power
dissipated in it.
13. When the same combination as the previous problem is connected to a battery, the potential difference
across the 10 resistor is found to be 50V. Find the potential differences across the other two resistors.
14. Draw a circuit diagram of three resistors with resistance 5, 10, and 20 in parallel. Find the
equivalent resistance. A potential difference of 60V is applied across the terminals of the combination.
For each resistor, calculate (a) the current through it, (b) the potential difference across it, and (c) the
power dissipated in it.
15. When the same combination as the previous problem is connected to a battery, the current through the
10 resistor is found to be 5.0A. Find the currents through the other two resistors.
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16. In the circuit below, the values of the resistances are given by R1 10 , R2  6, R3  3, and the emf
of the battery is 36 V.
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(a) Find the equivalent resistance, the voltage across each resistor, and the current through each
resistor.
(b) If the battery is switched over to the other side as shown, does the current through R1 change? If
so, what is its new value?
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17. In the circuit below, the values of the resistances are given by R1  2 , R2  4, R3  3, and the emf
of the battery is 12 V. Find the equivalent resistance, the voltage across each resistor, and the current
through each resistor.
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18. In the circuit below where the battery is ideal, find (a) the current in each resistor and (b) the power
delivered by the battery.
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19. The emf of a battery is 5 V and its internal resistance is 1 . The battery is connected to a load
resistance of 24. Find (a) the current, (b) the total power delivered by the battery, (c) the potential
difference across the load (terminal voltage), (d) the power dissipated in the load, and (e) the power
dissipated in the internal resistance.
20. The potential difference between the terminals of a battery is 12V when measured directly using a
voltmeter. When the battery is connected to a load of 240, the reading of the voltmeter becomes 9,6V.
What is the internal resistance of the battery? What load resistance should be used so the battery delivers
the most power to it? What is this maximum power?
Answers:
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1. 3.6MC, 12kWh
2. 0.28mm/s
3. 320 A / m 2 ,3.2  1013 m 3
4. 12.6km/s
5. a
6. 240m,0.21m
7. 3.46V, 3.50V, 0.0433V /m, 0.0714V /m
8. L ab
9. 180J
10. 2.4 A, 290W
11. (a) 576, 0.21A (b) lower, more
12. 35, 2A,10V, 20V, 40V,20W , 40W , 80W
13. 25V, 100V
14. 2.86,12A, 6A, 3A, 720W , 360W ,180W
15. 10A, 2.5A
16. (a)12, 30V, 6V,1A, 2A (b) Yes, 3.6A
17. 2, 4V,8V,12V, 2A,2A,4 A
18. (a)1.58A, 0.63A, 0.63A, 0.315A (b) 9.48W
19. 0.2A,1.0W , 4.8W , 0.96W , 0.04W ,
20. 60, 60, 0.6W
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