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In a resistive circuit Ohm's Law states that voltage is equal to

By Harold Washington,2014-05-06 17:33
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In a resistive circuit Ohm's Law states that voltage is equal to

Electricity Practice Problems June 17, 2010

Ohm’s Law Practice Problems

    In a resistive circuit, Ohm's Law states that: voltage is equal to current times resistance.

     Ohm's Law: V = I x R

     where:

     V = voltage (volts)

     I = current (amps)

     R = resistance (ohms)

    1) A circuit consists of a 10 ohm resistor and carries a 5 amp current. What is the

    voltage in the circuit (in volts)?

    2) One day, Olive has what she thinks is an ingenious idea to connect her dad‟s

    ammeter to a flashlight which uses a 6 volt battery. (An ammeter is a device that

    measures the current flow, in amps, in an electric circuit.) She connects the

    ammeter and sees that there is a current of 3 amps flowing in the circuit. What is

    the flashlight‟s resistance?

3) Olive built the circuit below with a variable-voltage power supply (the circuit‟s 1leftmost circuit element) and a resistor defined by the diagram below.

    resistor

    Using her ammeter (shown by the circuit element with an encircled „A‟), she took measurements of current passing through the resistor. She also used a voltmeter (as shown by the circuit element in the encircled „V‟) to measure the voltage across the resistor. She recorded these numerical values in a table, with the results shown below:

     1 Question adapted from http://www.allaboutcircuits.com/worksheets/ohm_law.html on 6/276/09.

    1

     Voltage Current

     0.66 V 0.22 A

     1.42 V 0.47 A

     2.54 V 0.84 A

     3.16 V 1.03 A

     4.51 V 1.50 A

     5.41 V 1.80 A

     5.99 V 2.00 A

     7.49 V 2.51 A

Plot the figures on the graph.

What mathematical relationship would you tell Olive that you see between voltage and

    current in this simple circuit?

4) A circuit is comprised of a battery and variable resistor, known as a rheostat (see

    figure). What happens to the current if resistance is doubled?

     a) Current doubles resistor

     b) Current halves

     c) Current remains the same

     d) The current goes to zero

    5) Which of the following statements is NOT true?

     a) Voltage is inversely proportional to the value of Resistance

     b) Voltage is directly proportional to current

     c) Current is inversely proportional to Resistance

     d) Voltage and Resistance are always proportional

    2

6) Olive‟s family car wouldn‟t start and she helped her father install a new 12-volt

    battery, but that did not fix the problem. Olive‟s dad then had the car towed to the

    auto mechanic‟s (Olive got to ride in the tow truck!), where the mechanic told her

    father that the car would need a new 600 amp start motor. Olive, wanting to show

    that she understood about such things, speaks up, and what does she proudly tell

    her father and the mechanic that she has figured out about the start motor?

Answers:

     1) V = I x R, or (5 amps) x (10 ohms) = 50 volts

     2) V = I x R which can be converted to R = V ? I, so:

     (6 volts) ? (3 amps) = (2 ohms)

     3) Current is linearly proportional to voltage, or equivalently, that the numerical

    value of the voltage is always three times that of the current, or equivalently,

    that the resistor has a value of three ohms which makes the current always one-

    third of the voltage.

     4) b

     5) a

     6) 0.02 ohm

    3

Electrical Power Law Practice Problems

    Power is the energy being used at a given instant in time and is measured in watts. In an electric circuit, power can be calculated by multiplying the circuit‟s voltage times

    its amperage:

     P = I x V (Power Law)

     P - Power consumed or produced by a circuit

     (watts, or equivalently: amp-volts)

7) How much power is consumed by

     a) The resistor in problem #1 above?

     b) The light bulb in problem #2?

     c) The start motor in problem #6?

    8) If voltage in household circuits is 120 volts, what is the current flow through a

     a) 60 watt incandescent light bulb?

     b) 12 watt CFL light bulb (which produces light approximately equal to a 60

    watt incandescent bulb)?

     c) 1500 watt hair drier?

    9) A circuit breaker is a safety device that protects a household electric circuit, such as all the electric outlets in a particular room in a house, from having too much electricity running through it. A breaker‟s function is to stop electric current flow

    when the current exceeds some preset maximum as given by the breaker‟s “rating”. What do Olive and her twin sister Penny have to do when they both dry their hair at the same time (assume that all of their house‟s bedroom circuit breakers are rated at

    15 amps and all bathroom circuit breakers are rated at 20 amps)?

    4

Answers:

7 a) 250 watts (50 volts x 5 amps)

     b) 18 watts (6 volts x 3 amps)

     c) 7200 watts (12 volts x 600 amps)

8) a) 0.5 amp (P = I x V ; I = P ? V)

     b) 0.1 amp

     c) 12.5 amps

    9) Since hair driers draw 12.5 amps each (from problem #8), only one hair drier at a time can operate from any single bedroom or bathroom circuit in the house without tripping a circuit breaker. Therefore, if the sisters need to both dry their hair at the same time they either use the same hair drier or they dry their hair in separate rooms.

    5

Electric “Power Company Law” Practice Problems

    Power consumption, which is also known as work, is defined as the total energy used or generated during a given period of time. In electrical circuits it is measured in kilowatt-hours (1000 watts of power lasting for one hour of time).

     W = P x t

     P - Power consumed by a circuit (typically measured in kilowatts)

     t - Amount of time that electric circuit operates

     Typically measured in hours for household use.

     W - Work, or equivalently: “total power used”

     Typically measured in kilowatt-hours (KWH),

     but also can be measured in watt-hours, where

     1 x KWH = 1000 x watt-hours.

     Assume 1 x KWH costs 20? on your monthly electric bill.

    Based on the above, you can calculate the cost of energy use for various electrical appliances and equipment if you have these three pieces of information:

     The rated power of the appliance, usually given in watts;

     The length of operating time,

     And the cost of electricity.

    10) a) How much power does a 100 watt light bulb use in a year if it is on a timer that

    turns on at 6:00 PM every night and off at midnight? (Assume there are

    approximately 9,000 hours in a year.)

     b) What is the cost of the electricity the bulb consumes in the course of a year?

     c) How much would be saved by switching the bulb to a 20 watt CFL bulb (which

    produces the same amount of light as the 100 watt bulb)?

    6

    11) a) When their dad pulls out the kitchen refrigerator to clean behind it, Olive sees a

    small metal plate on the back of the refrigerator that says it consumes 200 watts of

    power. During the cleaning, she notices that the refrigerator comes on for about

    four minutes every ten minutes or so. Later that day she tells her twin sister Penny

    what she has found out about the refrigerator, and after some figuring, what can

    Penny tell Olive about how much it costs to run the refrigerator for a year?

     b) Penny sees an on-line ad for a brand new “energy efficient” refrigerator that

    costs $1000. The ad claims the refrigerator costs only a dollar a day to run. Should

    Penny advise her family to replace their old refrigerator?

    12) Penny and Olive have a pet hamster named Max. The twins love to watch Max exercise by running in the spinner in his cage. For a science fair project, Penny got the idea to hook up Max‟s spinner to a fan blade that she disconnected from a handheld battery-operated personal electric fan. After she did so, she thought that when Max was running his very fastest that he was able to turn the fan blade about as fast as the blade had originally spun when attached to the electric fan.

     a) The fan could also be plugged into the wall using a power-supply that came with the fan. To help her sister with the science fair project, Olive connected the ammeter and voltmeter to the power supply while the fan was turning the blade and found that the fan operated at three volts and 0.5 amps. How much power did Max expend to turn the fan blade when it was attached to his spinner?

     For living things and for nutritional purposes, energy use is usually measured in

    Calories, with one nutritional Calorie being approximately equal to 0.001 KWH, or

    equivalently, there are approximately 1000 Calories per KWH.

    b) If Max always exercised after his dinner every day by jogging for six minutes on

    his spinner and assuming he was using one watt of power per second while doing

    so, how many Calories did he use to turn the blade during his after-dinner jog?

    c) What would be the equivalent electricity cost Max was capable of producing if he

    jogged for an hour? How much would this add up to for a year‟s worth of daily

    post-dinner jogging?

    7

    Answers:

10 a) 225 KWH

     W = P x t

     ? 24 hrs/day) x (9,000 hours/year)] = 225,000 watt-hours (100 watts) x [(6 hrs/day

     = 225 kilowatt-hours

     b) $45 (225 KWH per year) x ($0.20/KWH)

     c) $9 - the CFL consumes one-fifth the power of the 100 watt bulb, so its cost is 1/5.

    11 a) This problem is similar to 10a, but with the time usage in minutes for a ten-minute

    period, instead of for hours-per-day.

     (200 watts) x (4 minutes on ? 10 minutes) x (9,000 hrs/yr) = 720,000 watt-hours

     = 720 KWH

     720 KWH x $0.20/KWH = $142 per year of electricity usage.

     b) At a “dollar per day” that is probably about $365 per year, so the “energy efficient”

    refrigerator is costing over twice as much per year as the existing one, probably not a very

    good switch unless the new one is much, much larger or has some other major advantage.

12 a) 1.5 watts (P = I x V)

     b) Max used one watt of power for six minutes, which is equal to

     1 w X 0.1 hr = 0.1 w-hr = 0.0001 KWH (1w-hr = 0.001 KWH);

     this means he used 0.1 Calories (= 0.0001 KWH X 1000 Calories/KWH).

     c) Based on the answer to problem b above,

     0.0001 KWH/day X 365 days/yr = 0.365 KWH/yr

     At $0.20 / KWH, this means Max could generate the equivalent of

     approximately 7? worth of electricity in a year‟s worth of jogging.

    8

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