Chapter 20: Electric Current, Resistance, and Ohm's LawContent check — College Physics, Chapter 20: Electric Current, Resistance, and Ohm's Law

What is the current in milliamperes produced by the solar cells of a pocket calculator through which 4.00 C of charge passes in 4.00 h?

What is the current when a typical static charge of $0\text{.}\text{250}\mu \text{C}$ moves from your finger to a metal doorknob in $1.00\mu \text{s}$?

A large lightning bolt had a 20,000-A current and moved 30.0 C of charge. What was its duration?

(a) A defibrillator sends a 6.00-A current through the chest of a patient by applying a 10,000-V potential as in the figure below. What is the resistance of the path? (b) The defibrillator paddles make contact with the patient through a conducting gel that greatly reduces the path resistance. Discuss the difficulties that would ensue if a larger voltage were used to produce the same current through the patient, but with the path having perhaps 50 times the resistance. (Hint: The current must be about the same, so a higher voltage would imply greater power. Use this equation for power: $P=I^{2}R$.)

(a) A defibrillator passes 12.0 A of current through the torso of a person for 0.0100 s. How much charge moves? (b) How many electrons pass through the wires connected to the patient? (See figure two problems earlier.)

The batteries of a submerged non-nuclear submarine supply 1000 A at full speed ahead. How long does it take to move Avogadro’s number ($6\text{.}\text{02}\times {\text{10}}^{\text{23}}$) of electrons at this rate?

A large cyclotron directs a beam of ${\text{He}}^{\text{++}}$ nuclei onto a target with a beam current of 0.250 mA. (a) How many ${\text{He}}^{\text{++}}$ nuclei per second is this? (b) How long does it take for 1.00 C to strike the target? (c) How long before 1.00 mol of ${\text{He}}^{\text{++}}$ nuclei strike the target?

Using the results of the above example on Example 20.3, find the drift velocity in a copper wire of twice the diameter and carrying 20.0 A.

SPEAR, a storage ring about 72.0 m in diameter at the Stanford Linear Accelerator (closed in 2009), has a 20.0-A circulating beam of electrons that are moving at nearly the speed of light. (See Figure 20.35.) How many electrons are in the beam?

What current flows through the bulb of a 3.00-V flashlight when its hot resistance is $3\text{.}\text{60 Ω}$?

What is the effective resistance of a car’s starter motor when 150 A flows through it as the car battery applies 11.0 V to the motor?

(a) Find the voltage drop in an extension cord having a $0\text{.}\text{0600-}\Omega$ resistance and through which 5.00 A is flowing. (b) A cheaper cord utilizes thinner wire and has a resistance of $0\text{.}\text{300}\Omega$. What is the voltage drop in it when 5.00 A flows? (c) Why is the voltage to whatever appliance is being used reduced by this amount? What is the effect on the appliance?

What is the resistance of a 20.0-m-long piece of 12-gauge copper wire having a 2.053-mm diameter?

If the 0.010-mm diameter tungsten filament in a light bulb is to have a resistance of $\text{0.200 Ω}$ at $\mathrm{20.00º}\text{C}$, how long should it be?

What current flows through a 2.54-cm-diameter rod of pure silicon that is 20.0 cm long, when ${\mathrm{1.00\; \times \; 10}}^{\text{3}}\text{V}$ is applied to it? (Such a rod may be used to make nuclear-particle detectors, for example.)

A resistor made of Nichrome wire is used in an application where its resistance cannot change more than 1.00% from its value at $\text{20}\text{.}\mathrm{0º}\text{C}$. Over what temperature range can it be used?

An electronic device designed to operate at any temperature in the range from $\text{–10}\text{.}\mathrm{0º}\text{C to 55}\text{.}\mathrm{0º}\text{C}$ contains pure carbon resistors. By what factor does their resistance increase over this range?

Assuming a constant temperature coefficient of resistivity, what is the maximum percent decrease in the resistance of a constantan wire starting at $\text{20}\text{.}\mathrm{0º}\text{C}$?

A copper wire has a resistance of $0\text{.}\text{500}\Omega$ at $\text{20}\text{.}\mathrm{0º}\text{C}$, and an iron wire has a resistance of $0\text{.}\text{525}\Omega$ at the same temperature. At what temperature are their resistances equal?

Integrated Concepts

(a) Redo Exercise 20.25 taking into account the thermal expansion of the tungsten filament. You may assume a thermal expansion coefficient of $\text{12}\times {\text{10}}^{-6}/\text{ºC}$. (b) By what percentage does your answer differ from that in the example?

What is the power of a $1.00\times {\text{10}}^{\text{2}}\text{MV}$ lightning bolt having a current of ${\mathrm{2.00\; \times \; 10}}^{\text{4}}\text{A}$?

Find the power dissipated in each of these extension cords: (a) an extension cord having a $0\text{.}\text{0600}\text{-}\Omega$ resistance and through which 5.00 A is flowing; (b) a cheaper cord utilizing thinner wire and with a resistance of $0\text{.}\text{300}\Omega .$

Show that the units $1{\text{V}}^2/\Omega =1\text{W}$, as implied by the equation $P=V^2/R$.

Verify the energy unit equivalence that $1\text{kW}\cdot \text{h = 3}\text{.}\text{60}\times {\text{10}}^6\text{J}$.

An electric water heater consumes 5.00 kW for 2.00 h per day. What is the cost of running it for one year if electricity costs $\text{12.0 cents}\text{/kW}\cdot \text{h}$? See Figure 20.37.

What would be the maximum cost of a CFL such that the total cost (investment plus operating) would be the same for both CFL and incandescent 60-W bulbs? Assume the cost of the incandescent bulb is 25 cents and that electricity costs $\text{10 cents/kWh}$. Calculate the cost for 1000 hours, as in the cost effectiveness of CFL example.

Alkaline batteries have the advantage of putting out constant voltage until very nearly the end of their life. How long will an alkaline battery rated at $1\text{.}\text{00 A}\cdot \text{h}$ and 1.58 V keep a 1.00-W flashlight bulb burning?

The average television is said to be on 6 hours per day. Estimate the yearly cost of electricity to operate 100 million TVs, assuming their power consumption averages 150 W and the cost of electricity averages $\text{12}\text{.}0\text{cents/kW}\cdot \text{h}$.

00-gauge copper wire has a diameter of 9.266 mm. Calculate the power loss in a kilometer of such wire when it carries $1.00\times {\text{10}}^{\text{2}}\text{A}$.

Integrated Concepts

(a) What energy is dissipated by a lightning bolt having a 20,000-A current, a voltage of $1.00\times {\text{10}}^{\text{2}}\text{MV}$, and a length of 1.00 ms? (b) What mass of tree sap could be raised from $\text{18}\text{.}\mathrm{0º}\text{C}$ to its boiling point and then evaporated by this energy, assuming sap has the same thermal characteristics as water?

Integrated Concepts

How much time is needed for a surgical cauterizer to raise the temperature of 1.00 g of tissue from $\text{37}\text{.}\mathrm{0º}\text{C}$ to $\text{100º}\text{C}$ and then boil away 0.500 g of water, if it puts out 2.00 mA at 15.0 kV? Ignore heat transfer to the surroundings.

Integrated Concepts

(a) Assuming 95.0% efficiency for the conversion of electrical power by the motor, what current must the 12.0-V batteries of a 750-kg electric car be able to supply: (a) To accelerate from rest to 25.0 m/s in 1.00 min? (b) To climb a $2.00\times {\text{10}}^{\text{2}}\text{-m}$-high hill in 2.00 min at a constant 25.0-m/s speed while exerting $5.00\times {\text{10}}^{\text{2}}\text{N}$ of force to overcome air resistance and friction? (c) To travel at a constant 25.0-m/s speed, exerting a $5.00\times {\text{10}}^{\text{2}}\text{N}$ force to overcome air resistance and friction? See Figure 20.40.

Integrated Concepts

(a) An aluminum power transmission line has a resistance of $0\text{.}\text{0580}\Omega /\text{km}$. What is its mass per kilometer? (b) What is the mass per kilometer of a copper line having the same resistance? A lower resistance would shorten the heating time. Discuss the practical limits to speeding the heating by lowering the resistance.

Unreasonable Results

(a) What current is needed to transmit $1.00\times {\text{10}}^{\text{2}}\text{MW}$ of power at 480 V? (b) What power is dissipated by the transmission lines if they have a $1\text{.}\text{00}\text{-}\Omega$ resistance? (c) What is unreasonable about this result? (d) Which assumptions are unreasonable, or which premises are inconsistent?

Certain heavy industrial equipment uses AC power that has a peak voltage of 679 V. What is the rms voltage?

Military aircraft use 400-Hz AC power, because it is possible to design lighter-weight equipment at this higher frequency. What is the time for one complete cycle of this power?

In this problem, you will verify statements made at the end of the power losses for Example 20.10. (a) What current is needed to transmit 100 MW of power at a voltage of 25.0 kV? (b) Find the power loss in a $1\text{.}\text{00 -}\Omega$ transmission line. (c) What percent loss does this represent?

What is the peak power consumption of a 120-V AC microwave oven that draws 10.0 A?

Two different electrical devices have the same power consumption, but one is meant to be operated on 120-V AC and the other on 240-V AC. (a) What is the ratio of their resistances? (b) What is the ratio of their currents? (c) Assuming its resistance is unaffected, by what factor will the power increase if a 120-V AC device is connected to 240-V AC?

Find the time after $t=0$ when the instantaneous voltage of 60-Hz AC first reaches the following values: (a) $V_0/2$ (b) $V_0$ (c) 0.

(a) How much power is dissipated in a short circuit of 220-V AC through a resistance of $0\text{.}\text{250}\Omega$? (b) What current flows?

Find the current through a person and identify the likely effect on her if she touches a 120-V AC source: (a) if she is standing on a rubber mat and offers a total resistance of $\text{300 k}\Omega$; (b) if she is standing barefoot on wet grass and has a resistance of only $\text{4500}\Omega$.

Foolishly trying to fish a burning piece of bread from a toaster with a metal butter knife, a man comes into contact with 120-V AC. He does not even feel it since, luckily, he is wearing rubber-soled shoes. What is the minimum resistance of the path the current follows through the person?

(a) What is the resistance of a 220-V AC short circuit that generates a peak power of 96.8 kW? (b) What would the average power be if the voltage was 120 V AC?

Integrated Concepts

A short circuit in a 120-V appliance cord has a $0\text{.}\text{500}\text{-}\Omega$ resistance. Calculate the temperature rise of the 2.00 g of surrounding materials, assuming their specific heat capacity is $0.200\text{cal/g}\cdot º\text{C}$ and that it takes 0.0500 s for a circuit breaker to interrupt the current. Is this likely to be damaging?

Integrated Concepts

Use the ECG in Figure 20.31 to determine the heart rate in beats per minute assuming a constant time between beats.

Critical Thinking A copper wire of length 1.25 m is in a circuit. A current of 2.50 A flows through the wire. (a) Initially, the circuit is at $20.0\text{°}\text{C}$. If there is an energy loss of 3.25 MJ in the first second caused by the wire as soon as the circuit is turned on, what is the radius of the wire? (b) After the wire heats $3.000\text{°}\text{C}$, how much energy is being dissipated by the circuit per second? Neglect the effects of thermal expansion since the wire is considered to be physically constrained from expanding. Assume the current is maintained. (c) At what temperature will the energy dissipation be 1.00% higher than it was at the beginning of the experiment?