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Resistance and Ohm's Law

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Resistance and Ohm's Law Answer Key

Instructions: Read each question carefully. Choose the answer that best fits the question. If the question involves calculations, you must show all your math work.

1. 
Viviann was watching T.V., charging her iPod, heating up her curling iron, and blow-drying her hair. When she plugged in her super-deluxe make-up mirror with extra bright halogen bulbs the power went out and she caught a faint scent of burning rubber. What best explains what happened?
  1. Each device she added to the series circuit increased the total resistance. The voltage had to increase to provide current until it became so high it had to shut down.
  2. Every device she plugged in acted as a new resistor on a parallel circuit. This increased the resistance to the point that there was not enough voltage to power all the devices.
  3. Every device she plugged in acted as a new resistor on a parallel circuit. This would decrease the overall resistance on the parallel circuit and therefore increase the current flowing in the wires. Increasing the current generates more heat in the wire, causing a switch called a "circuit breaker" to open, stopping the flow of current in an attempt to prevent fire.
  4. Wizards obviously.
2. 
You invent a device that requires a minimum of 5 amps to operate, but can only handle a maximum of 8 amps without being destroyed. Assuming that it will be plugged into an outlet in the U.S. which has a voltage between 110 Volts and 120 Volts, what range of resistance can your object have to work safely?
  1. Between 15 Ohms and 22 Ohms
  2. Between 13.75 and 24 Ohms
  3. Between 30 and 40 Ohms
  4. None of the above
3. 
What is the relationship explained by Ohm's Law?
  • The current through a conductor between two points is directly proportional to the potential difference across the two points.
4. 
A resistor and voltage source are connected in a simple closed circuit, as shown here. The resistor obeys Ohm’s law.
Schematic of a Circuit
A. 
If the voltage, V, doubles but resistance stays the same, what happens to the current I? Explain your answer.
  • The current doubles because if you double a fraction’s numerator while leaving the denominator unchanged, you double the value of the fraction. Ohm’s law states that current equals voltage divided by resistance (I = V/R). Since V is the numerator, doubling the voltage drop will double the current.
B. 
If the resistance, R, doubles but the voltage remains unchanged, what happens to the current? Explain your answer.
  • The current is halved because if you double a fraction's denominator while leaving the numerator unchanged, you halve the value of the fraction. Ohm’s law states that current equals voltage divided by resistance (I = V/R). Since R is the denominator, doubling the resistance will halve the current.
5. 
Two simple closed circuits are constructed. Circuit A has a 6-V battery and a resistor on the wire drawing [math]24 Omega[/math]. Circuit B has the same voltage with a current of [math]0.3 A[/math]. If you compare the two circuits, which statement is correct about the amount of current?
  1. A carries a larger current than B.
  2. A carries a smaller current than B.
  3. A and B carry equal amounts of current.
  4. You cannot tell without more information.
6. 
A resistor with [math]R=101Omega[/math] is connected across a 1.50 V battery. How much current flows through the resistor?
  • [math]I=V/R=(1.5V)/(101Omega)=0.01485A[/math] or [math]0.0149A[/math]
7. 
Because of advances in lighting technology research, a halogen incandescent light bulb needs only 43 watts to produce the same amount of light as an "old-fashioned" 60-watt incandescent bulb. Both have a tungsten filament. How much more efficient is 43W halogen incandescent bulb, why is it able to last longer the 60W regular incandescent bulb, and how do you know what to buy to replace your old bulbs?
  • [math](43W)/(60W)=0.717 " or " 72%[/math] meaning a 28% reduction in energy produces the same light. A halogen bulb adds a halogen gas, creating a chemical reaction that generates more heat along the filament, causing a brighter light per watt ([math]620 " lumens" -: 43 W= 14.4(lm)/W[/math]), using only 0.35A of current. The halogen gas also regenerates evaporated tungsten (from the current going through the filament) and puts it back on the filament, extending the life of both the filament and the light bulb. The other incandescent, 60 watt bulb also produces 14.5 lm/W of light, but uses 0.50A of current. As a result, new bulbs are being labelled based on their light output, expressed in lumens, or with an equivalence claim, "43W = 60W", so that consumers are able to determine which new bulbs to buy.
8. 
Explain the relationship described by Ohm's Law in terms of mathematical proportionalities.
  • The equation I = V/R describes a relationship among the quantities where I is directly proportional to V, while I is inversely proportional to R.
9. 
If you connect three identical resistors in series and in parallel, in which case will they have a smaller equivalent resistance and why?
  • The resistors connected in parallel will have a smaller total resistance. The series resistors will have a total circuit resistance of 3R (the sum of all the resistors in series), whereas the parallel resistors will have a total circuit resistance of R/3 (the sum of all resistors in parallel divided by the number of resistors).

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