Electric Current Problems Answers 196b15

ELECTRIC CURRENT Mr. Charge’s Journey

PROBLEM #1 The amount of charge that es through the filament of a certain light bulb in 2 seconds is 1.67 C. A) What is the current in the light bulb? B) What is the number of electrons that through the filament in one second?

A)

Q 1.67 I   0.835 A t 2

B) In 2 s 1.67 C of charge es

In 1 s : 0.835C of charge will 1e  0.835C  -19 1.6  10 C 18  5.22  10 electrons

PROBLEM #2 1 x 1020 electrons flow through a conductor in 3 s. A) What is the charge flowing through the conductor? B) What is the current in the circuit?

A) # e  1  10 20 e

1.6  10 Q  1  10 e  1e Q  16C t  3s 20

19

C

Q 16 C B) I    5.33 A t 3s

PROBLEM #3

How many electrons a point in 5 s if a constant current of 8 A is maintained in a conductor?

I  8A Q? t  5s Q I t Q  I t  8  5 1e 20 #  40C   2.5  10 e 19 1.6  10

PROBLEM #4 The amount of charge that es through the filament of a certain light bulb in 2 seconds is 12C. A) What is the current in the light bulb? B) What is the number of electrons that through the filament in one second?

Q 12 A) I    6A t 2

B) Current of 6 A means 6 C of charge will through in 1 second.  6(6.25  10 )  3.75  10 electrons 18

19

PROBLEM #5 How many electrons a point in 10 s if a constant current of 20 A is maintained in a conductor?

I  20A Q? t  10s Q I t Q  I  t  20  10 #  200(6.25  10 )  1.25  10 e 18

21

PROBLEM #6 How many amperes of current flow in a wire through which 1018 electrons per second?

I? # electrons  1  10 Q? t  1s

18

19

Q  1  10 (1.6  10 )  .16C Q .16C I   .16 A t 1s 18

PROBLEM #7

The headlights of a typical car are powered by a 12 V battery. What is the resistance of the headlights if they draw 3 A of current when turned on?

I  3A V  12V R?

V 12 R   4 I 3

PROBLEM #8

Find the resistance of a portable lantern that uses a 24 V power supply and draws a current of 0.80 A.

I  .80 A V  24V R? V 24 R   30 I .80

PROBLEM #9

The current in a resistor of is 0.50 A when connected across a voltage of 120V. What is its resistance?

I  0.50 A V  120V R?

V 120 R   240 I 0.5

PROBLEM #10 An automobile headlight with a resistance of 30 ohms is placed across a 12 V battery. What is the current through the circuit?

I ? V  12V R  30

V 12 I   0.4 A R 30

PROBLEM #11 A motor with an operating resistance of 32 ohms is connected to a voltage source. The current in the circuit is 3.8 A. What is the voltage of the voltage source?

I  3.8 A V ? R  32

V  IR  3.8(32)  121.6V

PROBLEM #12 A transistor radio uses 0.0002 A of current, when a 3 V battery operates it. What is the resistance of the radio circuit?

I  0.0002 A V  3V R? V 3 R   15000 I 0.0002

PROBLEM #13 What is the resistance of an electric frying pan that draws 12 amperes of current when connected to a 120 V circuit?

I  12 A V  120V R? V 120 R   10 I 12

PROBLEM #14 How much current is drawn by a lamp that has a resistance of 100 ohms when a voltage of 50 volts is impressed across it?

I ? V  50V R  100

V 50 I   0.5 A R 100

PROBLEM #15 The plate on a certain steam iron states that the iron carries a current of 6.4 A when connected to a 120 V source. What is the resistance of the steam iron?

I  6.4 A V  120V R? V 120 R   18.75 I 6.4

PROBLEM #16 The resistance of the hot plate is 48 ohms. How much current does the plate carry when connected to a 120 V source?

I ? V  120V R  48

V 120 I   2.5 A R 48

EXAMPLE 1 A heater has a resistance of 10 . It operates on 120 V. A) What is the current through the resistance? B) What thermal energy is supplied to the heater in 10 s?

V 120 I   12 A R 10 E  Pt  VIt  120(12)(10)  14400J

EXAMPLE 2

A current of 6 A flows through a resistance of 300  for one hour. What is the power loss? How much heat is generated in joules?

V  IR  6(300)  1800V P  VI  1800(6)  10800W E  Pt  10800W (3600s)  3.8  10 J 7

PROBLEM #17 A 15 ohm electric heater operates on a 120 V outlet. A) What is the current through the heater? B) How much energy does the heater liberate in 30 seconds? C) How much thermal energy does the heater liberate in this time?

V 120 I   8A R 15 E  Pt  VIt  120(8)(30)  28800J

PROBLEM #18 A 30-ohm resistor is connected across a 60 V battery. A) What is the current in the circuit? B) How much energy does the resistor use in 5 minutes?

V 60 I   2A R 30 E  Pt  VIt  60(2)(5)(60)  36000J

PROBLEM #19

A soldering iron draws 0.75 A at 120 V. How much energy does the resistor use in 15 minutes?

E  Pt  VIt  120(.75)(15)(60)  81000J

PROBLEM #20

An electric lamp has an 80 ohm filament connected to a 110 V direct current line. What is the current through the filament? What is the power loss in watts?

V 110 I   1.375 A R 80 P  VI  110(1.375)  151.25 W

PROBLEM #21

How much does it cost to burn 100 W light bulb for 24 hours if the electrical energy costs $0.08 per kilowatt-hour?

P  100 W  0.1kW t  24h E  Pt  0.1kW(24h)  2.4kWh $.08 Cost  2.4kWh( )  $0.192 kWh

PROBLEM #22 A modern color TV set draws 2 A when operated on 120 V. A) How much power does the set use? B) If the set is operated for an average of 7 hours/day, what energy in kWh does it consume per month (30 days) C) At $0.11 per kWh, what is the cost of operating the set per month?

P  VI  120V (2 A)  240 W  .240kW E  Pt B)  .240kW(7)(30h)  50.4kWh $.11 )  $5.544 C) Cost  50.4kWh( kWh A)

PROBLEM #23 An electric space heater draws 20 A from a 120V source. It is operated on the average of 5 hours each day. A) How much power does the heater use? B) How much energy in kWh does it consume in 30 days? C) At $.11 per kWh, what does it cost to operate it for 30 days?

P  VI  120(20)  2400 W  2.4kW E  Pt B)  VIt  2.4kW(5)(30h)  360kWh C) Cost  360(.11kWh) A)

PROBLEM #24 A digital clock has an operating resistance of 12,000 ohms and is plugged into a 115 V outlet. Assume the clock obeys ohm’s law. A) How much current does it draw? B) How much power does it use? C) If the owner of the clock pays $0.09 per kWh, what does it cost to operate the clock for 30 days?

A)

V 115 I   .0096A R 12000 P  VI  115(.0096)  1.1W  .0011kW B) E  Pt  .0011kW(24)(30h)  .792kWh $.09 C) Cost  .792kWh( )  $.07 kWh

PROBLEM #25

An electric heater is rated 500 W. A) How much energy is delivered to the heater in half an hour?

P  500 W  .5kW E  Pt  .5kW(.5h)  .25kWh or 60 sec E  500 W (30 min)( ) 1 min  900000Ws  900000J

PROBLEM #26

Each coil in a resistance box is capable of dissipating heat at rate of 4 W. What is the maximum current that should be allowed across the coil to avoid overheating if the coil has of 2 ohms?

P  4W R  2 P  VI  ( IR)( I ) P  I R 2

I

P 4   1.41A R 2

PROBLEM #27

How much does it cost to run a 2 W clock for one year (365.25 days) if it costs 3.53 cents per kWh?

P  2 W  .002kW E  Pt  .002kW(24h)(365.25)  17.532kWh $.0353 Cost  17.532kWh( ) kWh  $.62

PROBLEM #28 A small electric furnace that expends 2 kW of power is connected across a potential difference of 120 V. A) What is the current in the circuit? B) What is the resistance of the furnace? C) What is the cost of operating the furnace for 24 hours at 7 cents per kWh?

A)

P  2kW V  120V P 2000W I   16.7 A V 120V V 120V R   7.18 I 16.7 A

E  Pt  2kW(24hr )  48kWhr $.07 )  $3.36 C) Cost  48kWh( kWh

B)