**PHY 2049**

**
Electric Resistance & Circuits**

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**Physics requires practice to develop your solving problems
skills and your logical thinking . I strongly recommend to study carefully the

examples, and solve the following problems *in
your book*

Examples: 27.3 -27.6 Pages 839 - 843; 28.8- 28.9 Pages 871 - 873

Problems 13,15,17,21,23,29,31,33,35 Page 852 - 3 ; 21,24,26,27,29,30 Page 887 - 8

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**
Electric
Resistance**

1.
(1E)
Find the resistance of 78.0 m of No 20 aluminum wire at 20^{0} C (
r
= 2.83x 10^{-6}
W
cm, A= 2.07x 10^{-2} cm^{2} .)

2. (8E) Find the length of copper wire with resistance 0.0262 W /ft and total resistance 3.00 W.

3.
(9E)
Find
the cross sectional area of copper wire at 20 ^{0} C that is 60.0 m long
and has resistivity
r
= 1.72 x 10^{-6}
W
cm and resistance 0.788
W.

4. (10E)Find the length of a copper wire with resistance 0.0262 W /ft and total resistance 5.62 W.

5. (1G) A current of 1.30 A flows in a wire. How many electrons are flowing past any point in the wire per second?

6. (2G) A service station charges a battery using a current of 6.7 A for 5.0 h. How much charge passes through the battery?

7. (4G) What is the resistance of a toaster if 120 V produces a current of 4.2 A?

8 (5G) What voltage will produce 0.25 A of current through a W. resistor?

9.
(6G)
A hair dryer draws 7.5 A
when plugged into a 120-V line. (*a*) What is its resistance? (*b*)
How much charge passes through it in 15 min? (Assume direct current.)

10. (13G) What is the resistance of a 3.5-m length of copper wire 1.5 mm in diameter?

11.
(9G)
A bird stands on a dc
electric transmission line carrying 2800 A . The line has 2.5
x 10^{-5 }
W
resistance
per meter, and the bird’s feet are 4.0 cm apart. What is the potential
difference between the bird’s feet?

12. (15G) Can a 2.5-mm-diameter copper wire have the same resistance as a tungsten wire of the same length? Give numerical details.

13.
(19G**.**
A 100-W light bulb has a
resistance of about W,
when
cold (20°C) and W when
on (hot). Estimate the temperature of the filament when hot assuming an average
temperature coefficient of
0.0060 ( C ^{0})^{-1}

14. (17G) How much would you have to raise the temperature of a copper wire (originally at 20°C) to increase its resistance by 15%?

15. (20G) Compute the voltage drop along a 26-m length of household no. 14 copper wire (used in 15-A circuits). The wire has diameter 1.628 mm and carries a 12-A current.

16. (23G) A length of aluminum wire is connected to a precision 10.00-V power supply, and a current of 0.4212 A is precisely measured at 20.0°C. The wire is placed in a new environment of unknown temperature where the measured current is 0.3618 A. What is the unknown temperature?

17.
(32G)
You buy a 75-W light bulb
in Europe, where electricity is delivered to homes at 240 V. If you use the
light bulb in the United States at 120 V (assume its resistance does not
change), how bright will it be relative to 75-W 120-V bulbs? [*Hint*:
assume roughly that brightness is proportional to power consumed.]

18.
(37G)**
**How many 100-W
light bulbs, connected to 120 V as in Fig. 18–20, can be used without blowing a
15-A fuse?

19. (38G) An extension cord made of two wires of diameter 0.129 cm (no. 16 copper wire) and of length 2.7 m (9 ft) is connected to an electric heater which draws 15.0 A on a 120-V line. How much power is dissipated in the cord?

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**
Electric
Circuits**

20. (5G) Four W light bulbs are connected in series. What is the total resistance of the circuit? What is their resistance if they are connected in parallel?

21.
(6G)
Three
W light
bulbs and three
W
light
bulbs are connected in series. (*a*) What is the total resistance of the
circuit? (*b*) What is their resistance if all six are wired in parallel?

22.
(13G) Eight identical lights are connected in series
across a 110-V line. (*a*) What is the voltage across each bulb? (*b*)
If the current is 0.50 A, what is the resistance of each bulb, and what is the
power dissipated in each?

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23(3S). **
Two 1.50-V batteries—with their positive terminals in
the same direction—are inserted in series into the barrel of a flashlight. One
battery has an internal resistance of 0.255 **Ω**, the other an internal
resistance of 0.153 **Ω**. When the switch is closed, a current of 600 mA
occurs in the lamp. (a) What is the lamp’s resistance? (b) What fraction of the
chemical energy transformed appears as internal energy in the batteries?

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**

24
(1E) The
current in a loop circuit that has a resistance of *R*_{1} is 2.00
A. The current is reduced to 1.60 A when an additional resistor *R*_{2}
= 3.00 **Ω** is added in series with *R*_{1}. What is the value
of *R*_{1}?

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25 **
(S6)
**(a) Find the equivalent resistance
between points *a *and *b *in Figure P28.6. (b) A potential difference
of 34.0 V is applied between points *a *and *b*. Calculate the current
in each resistor.

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**

26(6S).Consider
the circuit shown in Figure P28.9. Find (a) the current in the 20.0-**Ω**
resistor and (b) the potential difference between points *a *and *b*.

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**

27(
11S)** **Three 100-**Ω** resistors are
connected as shown in Figure P28.11. The maximum power that can safely be
delivered to any one resistor is 25.0 W. (a) What is the maximum voltage that
can be applied to the terminals *a *and *b*? For the voltage
determined in part (a), what is the power delivered to each resistor? What is
the total power delivered?

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28(1S)
** **Calculate
the power delivered to each resistor in the circuit shown in Figure P28.15.

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29(19S) ** **Four
resistors are connected to a battery as shown in Figure P28.19. The current in
the battery is *I*, the battery emf is *
ε*,
and the resistor values are *R*_{1}
= *R*, *R*_{2}
= 2*R*, *R*_{3}
= 4*R*, *R*_{4}
= 3*R*. (a) Rank the resistors according to the potential difference across
them, from largest to smallest. Note any cases of equal potential differences.
(b) Determine the potential difference across each resistor in terms of
*ε*.
(c) Rank the resistors according to the current in them, from largest to
smallest. Note any cases of equal currents. (d) Determine the current in each
resistor in terms of *I*. (e) **What If? **If *R*_{3}
is increased, what happens to the current in each of the resistors? (f) In the
limit that *R*_{3}
∞,
what are the new values of the current in each resistor in terms of *I*,
the original current in the battery?**
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30(5G) light bulbs are connected in series. What is the total resistance of the circuit? What is their resistance if they are connected in parallel?

31(6G) Three
light
bulbs
and three light
bulbs
are connected in series. (*a*) What is the total resistance of the circuit?
(*b*) What is their resistance if all six are wired in parallel?

32(7G) A and a resistor are connected in series with a 12-V battery. What is the voltage across the resistor?

33.(17G) Determine (*a*)
the equivalent resistance of the circuit shown in Fig. 19–39, and (*b*) the
voltage across each resistor.

34(19G) Consider the
network of resistors shown in Fig. 19–40. Answer qualitatively: (*a*) What
happens to the voltage across each resistor when the switch S is closed? (*b*)
What happens to the current through each when the switch is closed? (*c*)
What happens to the power output of the battery when the switch is closed? (*d*)
Let and
Determine
the current through each resistor before and after closing the switch. Are your
qualitative predictions confirmed?

35 (20 G) What is the net resistance of the circuit connected to the battery in Fig. 19–41? Each resistance has

**Kirchhoff's
Rules**

36**(20S)
****
**The
ammeter shown in Figure P28.20 reads 2.00 A. Find *I*_{1},
*I*_{2},
and *
ε*.

*
*

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37 ( 21S)**
Determine
the current in each branch of the circuit shown in Figure P28.21.

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**

38 ( 24S) ** ****
**Using
Kirchhoff’s rules, (a) find the current in each resistor in Figure P28.24. (b)
Find the potential difference between points *c *and *f. *Which point
is at the higher potential?

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**

39** **( 26S)**
****
**In the
circuit of Figure P28.26, determine the current in each resistor and the voltage
across the 200-**Ω** resistor.

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40 (29S)
For the circuit shown in Figure P28.29, calculate (a) the current in the 2.00-**Ω**
resistor and (b) the potential difference between points *a *and *b.*

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41 ( 30S)** **
** ****
**Calculate
the power delivered to each resistor shown in Figure P28.30.

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42 ( 27 G) Determine the magnitudes and directions of the currents through and in Fig. 19–47.

43 ( 29G) Determine the magnitudes and directions of the currents in each resistor shown in Fig. 19–48. The batteries have emfs of and and the resistors have values of and the resistors have values of and

44.( 31 G) Calculate the currents in each resistor of Fig. 19–49.

45( 32G) (*a*)
Determine the currents and
in
Fig. 19–50. Assume the internal resistance of each battery is
(*b*)
What is the terminal voltage of the 6.0-V battery?

**
RC Circuits**

46.**(31S)**
Consider a series *RC *circuit (see Fig.
28.19) for which *R *= 1.00 M**Ω**, *C *= 5.00 *μ*F, and
*ε*
= 30.0 V. Find (a) the time constant of the circuit and (b) the maximum charge
on the capacitor after the switch is closed. (c) Find the current in the
resistor 10.0 s after the switch is closed.

47.(32S**)
**** **A
2.00-nF capacitor with an initial charge of 5.10 *μ*C is discharged through
a 1.30-k**Ω** resistor. (a) Calculate the current in the resistor 9.00 *μ*s
after the resistor is connected across the terminals of the capacitor. (b) What
charge remains on the capacitor after 8.00 *μ*s? (c) What is the maximum
current in the resistor?

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48.(33S)** **
A fully charged capacitor stores energy
*U*_{0}.
How much energy remains when its charge has decreased to half its original
value?

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49.(34S)**
**
A
capacitor in an *RC *circuit is charged to 60.0% of its maximum value in
0.900 s. What is
the time constant of the circuit?

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50.(36S**)****
**In the circuit of Figure P28.36, the switch S has
been open for a long time. It is then suddenly closed. Determine the time
constant (a) before the switch is closed and (b) after the switch is closed. (c)
Let the switch be closed at *t *= 0. Determine the current in the switch as
a function of time.

51.(49G)
(I) Electrocardiographs are often connected as shown in Fig. 19–55. The leads
are said to be capacitively coupled. A time constant of 3.0 s is typical and
allows rapid changes in potential to be recorded accurately. If
what
value must *R* have? [*Hint*: consider each leg as a separate
circuit.]

52.(51G) In
Fig. 19–56 (same as Fig. 19–20a), the total resistance is
and
the battery’s emf is 24.0 V. If the time constant is measured to be
calculate
(*a*) the total capacitance of the circuit and (*b*) the time it takes
for the voltage across the resistor to reach 16.0 V after the switch is closed.

53.(51G). The
*RC* circuit of Fig. 19–57 (same as Fig. 19–21a) has
and
The
capacitor is at voltage at
when
the switch is closed. How long does it take the capacitor to discharge to 1.0%
of its initial voltage?

54.(52G) Two
resistors and two uncharged capacitors are arranged as shown in Fig. 19–58. Then
a potential difference of 24 V is applied across the combination as shown. (*a*)
What is the potential at point a with switch S open? (Let
at
the negative terminal of the source.) (*b*) What is the potential at point
b with the switch open? (*c*) When the switch is closed, what is the final
potential of point b? (*d*) How much charge flows through the switch S
after it is closed?

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