Chapter 18: Electric Currents

The resistance of a wire is defined as the ratio of voltage to current. This is based on Ohm's Law, which states that the current flowing through a conductor is directly proportional to the voltage applied across it and inversely proportional to its resistance. Therefore, the correct answer is (voltage)/(current), as it represents the relationship between voltage and current in determining the resistance of a wire.

The current drawn by the lamp can be calculated using Ohm's Law, which states that current (I) is equal to the power (P) divided by the voltage (V). In this case, the power is 150 W and the voltage is 120 V. Dividing 150 by 120 gives us a current of 1.25 A.

The hair dryer is rated at 1200 W, which means it consumes 1200 watts of power when operating. To find the current it draws, we can use the formula P = IV, where P is power, I is current, and V is voltage. Rearranging the formula to solve for I, we have I = P/V. Plugging in the values, we get I = 1200 W / 110 V = 10.91 A, which can be rounded to 11 A. Therefore, the hair dryer will draw a current of 11 A.

The current drawn by a device can be calculated using Ohm's Law, which states that current (I) is equal to the power (P) divided by the voltage (V). In this case, the power of the light bulb is given as 150 W and the voltage is given as 110 V. Therefore, the current can be calculated as 150 W / 110 V = 1.36 A. Rounding this to the nearest tenth gives us 1.4 A, which is the correct answer.

The annual cost to operate the bulb can be estimated by calculating the total energy consumed by the bulb in a year and multiplying it by the cost per kilowatt-hour. The bulb is on for 10 hours per day, so it consumes 100 watts x 10 hours = 1000 watt-hours or 1 kilowatt-hour per day. In a year, it would consume 1 kilowatt-hour x 365 days = 365 kilowatt-hours. Multiplying this by the cost per kilowatt-hour, which is 10 cents, gives us 365 kilowatt-hours x $0.10 = $36.50. Therefore, the annual cost to operate the bulb is $36.50.

The voltage across a resistor can be calculated using Ohm's Law, which states that voltage (V) is equal to current (I) multiplied by resistance (R). In this case, the current is given as 5.0 A and the resistance is 5.0 Ω. By multiplying these values together, we get 25 V as the voltage across the resistor.

To find the length of the copper wire needed, we can use the formula for resistance: R = (ρ * L) / A, where R is the resistance, ρ is the resistivity, L is the length, and A is the cross-sectional area. Rearranging the formula to solve for L, we get L = (R * A) / ρ.

Given that the resistance is 15 Ω and the diameter is 0.15 mm, we can calculate the cross-sectional area using the formula A = π * (d/2)^2, where d is the diameter. Plugging in the values, we get A = π * (0.15 mm/2)^2.

Substituting the values of R, A, and ρ into the formula for L, we find L = (15 Ω * π * (0.15 mm/2)^2) / (1.68 * 10^(-8) Ω*m).

After performing the calculations, we find that L is approximately 16 meters. Therefore, the correct answer is 16 m.

1 W is equivalent to 1 V*A because power (W) is calculated by multiplying voltage (V) and current (A). Therefore, 1 V*A is the correct unit for 1 W.

To calculate the potential difference required to cause a current of 4.00 A to flow through a resistance of 330 Ω, we can use Ohm's Law, which states that V = I * R, where V is the potential difference, I is the current, and R is the resistance. Plugging in the given values, we get V = 4.00 A * 330 Ω = 1320 V. Therefore, the correct answer is 1320 V.

The voltage drop along the length of the bus bar can be calculated using Ohm's Law, which states that V = I * R, where V is the voltage drop, I is the current, and R is the resistance. The resistance of the bus bar can be calculated using the formula R = (ρ * L) / A, where ρ is the resistivity of copper, L is the length of the bus bar, and A is the cross-sectional area of the bus bar. Plugging in the given values, we can calculate the resistance and then use it to calculate the voltage drop. The correct answer, 0.067 V, is the result of this calculation.

The maximum voltage that can be applied across a 200-Ω resistor rated at 1/4 W is 7.1 V. This can be calculated using the formula P = V^2/R, where P is the power in watts, V is the voltage in volts, and R is the resistance in ohms. Rearranging the formula to solve for V, we get V = sqrt(P*R). Plugging in the values of P = 1/4 W and R = 200 Ω, we find V = sqrt(1/4 * 200) = sqrt(50) = 7.1 V.

The resistance of an electrical device can be calculated using Ohm's Law, which states that resistance (R) is equal to the voltage (V) divided by the current (I). In this case, the voltage is given as 110 V and the power of the soldering iron is given as 25 W. Since power is equal to the square of the current multiplied by the resistance (P = I^2 * R), we can rearrange the equation to solve for resistance. Rearranging the equation gives us R = P/V^2. Plugging in the values, we get R = 25/110^2 = 0.0020 Ω. However, the answer options are given in kilohms, so we convert 0.0020 Ω to kilohms by dividing by 1000, giving us 0.0020/1000 = 0.000002 kΩ. Rounded to two decimal places, this is approximately equal to 0.48 kΩ. Therefore, the correct answer is 0.48 kΩ.

A coulomb per second is the unit of electric current, which is measured in amperes. Therefore, a coulomb per second is the same as an ampere.

The amount of charge passing through a point is equal to the current multiplied by the time. In this case, the current is 0.50 A and the time is 10 s. Therefore, the amount of charge passing through the point is 0.50 A x 10 s = 5.0 C.

The symbol Ω represents the unit of electrical resistance, also known as ohm. The correct answer, 1 V/A, represents the unit of electrical resistance, which means that 1 volt per ampere is equivalent to 1 ohm.

The resistivity of most common metals increases as the temperature increases. This is because as the temperature rises, the atoms in the metal vibrate more vigorously, causing more collisions between the electrons and the atoms. These collisions impede the flow of electrons, resulting in an increase in resistivity. Therefore, as the temperature increases, the resistance of the metal also increases.

The cost to run the computer annually can be calculated by multiplying the power consumption (400 W) by the number of hours it is turned on per day (8.0 hours), then multiplying by the number of days in a year (365 days). Finally, divide by 1000 to convert from watts to kilowatts and multiply by the cost of electricity per kilowatt-hour (10 cents). Therefore, the cost to run the computer annually is $116.80.

The direction of conventional current is taken to be the direction that positive charges would flow. This convention was established before the discovery of electrons and is still used today. It simplifies the analysis of circuits and allows for consistent understanding and communication in the field of electrical engineering.

The resistance of a device can be calculated using Ohm's law, which states that resistance (R) is equal to voltage (V) divided by current (I). In this case, the voltage is given as 110 V and the current is given as 1.40 A. By dividing 110 V by 1.40 A, we get a resistance of 78.6 Ω.

The motor has a power output of 2.0 hp, which is equivalent to 1492 W (2.0 hp * 746 W/hp). The efficiency of the motor is given as 60%, which means that 60% of the input power is converted into useful work, while the remaining 40% is lost as heat or other forms of energy. Therefore, the input power to the motor can be calculated by dividing the output power by the efficiency: Input power = Output power / Efficiency = 1492 W / 0.60 = 2486.67 W. The current drawn from the 120-V line can be calculated using the formula: Current (A) = Power (W) / Voltage (V) = 2486.67 W / 120 V = 20.72 A, which can be rounded to 21 A.

The cost can be calculated by first finding the total energy used, which is equal to the product of current, resistance, and time. In this case, it is given that 14 A of current flows through 8.0 Ω for 24 hours. Therefore, the total energy used is 14 A * 8.0 Ω * 24 hours. To convert this energy to kilowatt-hours (kWh), we divide by 1000. Finally, we multiply the energy in kWh by the cost per kWh, which is $0.09. Thus, the cost is $3.39.

The voltage across the wire can be calculated using Ohm's Law, which states that V = I * R, where V is the voltage, I is the current, and R is the resistance. The resistance of the wire can be calculated using the formula R = (ρ * L) / A, where ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire. Plugging in the given values, we can calculate the resistance of the wire. Finally, by multiplying the resistance with the current, we can find the voltage across the wire, which is 0.64 V.

A 100-W light bulb uses 0.1 kWh (kilowatt-hour) of energy in 1 hour. To find out how much energy it uses in 8.0 hours, we multiply 0.1 kWh by 8, which gives us 0.8 kWh. Therefore, the correct answer is 0.80 kWh.

A current that is sinusoidal with respect to time is referred to as an alternating current. This is because an alternating current continuously changes direction, oscillating back and forth in a sinusoidal pattern. In contrast, a direct current flows in only one direction without changing. Therefore, the given correct answer accurately describes the nature of a sinusoidal current.

The current flowing can be calculated using the formula I = Q/t, where I is the current, Q is the charge, and t is the time. In this case, the charge is given as 0.67 C and the time is given as 0.30 s. Plugging these values into the formula, we get I = 0.67 C / 0.30 s = 2.2 A. Therefore, the correct answer is 2.2 A.

The cost of running the central air-conditioning unit can be calculated by multiplying the power (5000 W) by the time (2.0 hr/day) and dividing by 1000 to convert to kilowatt-hours (kWh). This gives us 10 kWh. The cost of running the light bulbs can be calculated by multiplying the power (60 W) by the time (5.0 hr/day) and dividing by 1000 to convert to kWh. This gives us 0.3 kWh. Adding these two values together gives us a total of 10.3 kWh. Finally, multiplying this by the cost of electricity (8.0 ¢ per kWh) gives us a total cost of $31.20.

The nominal resistance of a 100-W light bulb designed to be used in a 120-V circuit can be calculated using Ohm's law, which states that resistance is equal to voltage divided by current. In this case, the power of the light bulb is given as 100 W and the voltage as 120 V. Using the formula P = V^2 / R, we can rearrange it to solve for resistance: R = V^2 / P. Plugging in the values, we get R = (120 V)^2 / 100 W = 144 Ω. Therefore, the correct answer is 144 Ω.

The resistance of the heating element can be calculated using Ohm's law, which states that resistance is equal to voltage divided by current. In this case, the voltage is given as 120 V and the power is given as 800 W. Using the formula P = V^2/R, we can rearrange it to solve for resistance: R = V^2/P. Plugging in the values, we get R = (120^2)/800 = 18 Ω. Therefore, the correct answer is 18 Ω.

The net number of electrons that have passed through the coffee maker can be calculated using the formula:

Net number of electrons = (current * time) / (charge of an electron)

Given that the current is 13.5 A and the time is 10 min (which is equal to 600 s), we can substitute these values into the formula:

Net number of electrons = (13.5 A * 600 s) / (1.6 * 10^-19 C)

Simplifying this expression gives us:

Net number of electrons = 5.1 * 10^22

Therefore, the correct answer is 5.1 * 10^22.

When the resistance in a constant voltage circuit is doubled, the power dissipated by the circuit decreases to one-half its original value. This is because power is directly proportional to the square of the resistance (P = V^2/R), so when the resistance is doubled, the power is reduced by a factor of four. Therefore, the correct answer is that the power dissipated by the circuit decreases to one-half its original value.

The resistance of a wire is directly proportional to its length, meaning that as the length of the wire increases, the resistance also increases. Additionally, the resistance is inversely proportional to the cross-sectional area of the wire, meaning that as the cross-sectional area increases, the resistance decreases. This relationship is described by Ohm's Law, which states that resistance (R) is equal to the resistivity (ρ) of the material multiplied by the length (L) of the wire divided by the cross-sectional area (A) of the wire. Therefore, the correct answer is that the resistance of a wire is proportional to its length and inversely proportional to its cross-sectional area.

Negative temperature coefficients of resistivity exist in semiconductors. This means that the resistivity of semiconductors decreases as the temperature increases. In semiconductors, the increase in temperature leads to an increase in the number of charge carriers, which in turn decreases the resistivity. This behavior is opposite to that of conductors and superconductors, where the resistivity generally increases with increasing temperature.

Car batteries are rated in "amp-hours" because it is a measure of the amount of charge the battery can deliver over a certain period of time. Amp-hours represent the capacity of the battery to provide a certain amount of electric current for a specific duration. It indicates how long the battery can sustain a particular level of current before it is fully discharged. Therefore, the rating in amp-hours is directly related to the battery's charge capacity.

The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. In this case, the length of the wire is given as 1.0 m. To calculate the cross-sectional area, we need to first convert the diameter of the wire from inches to meters. The diameter is given as 0.40 in, which is equal to 0.01 m. The radius of the wire is half the diameter, so the radius is 0.005 m. The cross-sectional area can be calculated using the formula A = πr^2, where A is the cross-sectional area and r is the radius. Plugging in the values, we get A = π(0.005)^2 = 0.0000785 m^2. Now we can calculate the resistance using the formula R = ρL/A, where R is the resistance, ρ is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area. Plugging in the values, we get R = (1.68 * 10^(-8) Ω*m)(1.0 m)/(0.0000785 m^2) = 0.00021 Ω. Therefore, the correct answer is 0.00021 Ω.

The rms current flowing through a device can be calculated using Ohm's Law, which states that current (I) is equal to power (P) divided by voltage (V). In this case, the power is given as 500 W and the voltage is 120 V. By substituting these values into the formula, we can calculate the current as 500 W / 120 V = 4.2 A. Therefore, the correct answer is 4.2 A.

A 1.0 cm diameter rod has a smaller cross-sectional area compared to a 2.0 cm diameter rod. Resistance is directly proportional to the cross-sectional area, so a smaller cross-sectional area results in higher resistance. The resistance of the 1.0 cm diameter rod is 300% more than the resistance of the 2.0 cm diameter rod.

The resistance of a carbon resistor increases with an increase in temperature. The given question provides the temperature coefficient of resistivity for carbon, which is -5.0 * 10^(-4) /C°. This means that for every 1°C increase in temperature, the resistance of the carbon resistor will decrease by 5.0 * 10^(-4) Ω. Since the temperature has increased from 20°C to 120°C, there is a 100°C increase in temperature. Therefore, the resistance will decrease by (5.0 * 10^(-4) * 100) Ω, which equals 0.05 Ω. Subtracting this from the initial resistance of 18 Ω gives us a final resistance of 17 Ω.

The cost of the battery is given as $1.49 and it runs the CD player for 6.0 hours. The current supplied by the battery is 25 mA. To find the cost of energy in dollars per kWh, we need to calculate the energy consumed by the CD player in kWh.

First, we need to convert the current from mA to A by dividing it by 1000. So, the current is 0.025 A.

Next, we can calculate the energy consumed by multiplying the voltage (9.0 V) by the current (0.025 A) and the time (6.0 hours). This gives us an energy of 1.35 Wh (watt-hours).

To convert this to kWh, we divide by 1000, giving us 0.00135 kWh.

Finally, we can calculate the cost of energy per kWh by dividing the cost of the battery ($1.49) by the energy consumed (0.00135 kWh). This gives us a cost of $1100/kWh.

The resistance of a wire is inversely proportional to its cross-sectional area. Therefore, if one wire has twice the cross-sectional area of the other, it means that it has half the resistance. This is because a larger cross-sectional area allows for more space for the flow of electrons, resulting in less resistance to the current. Thus, the thicker wire will have half the resistance of the shorter wire.

The potential difference between two points in a conductor can be calculated using Ohm's Law, which states that V = I * R, where V is the potential difference, I is the current, and R is the resistance. In this case, the resistance can be determined using the formula R = (ρ * L) / A, where ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire. Given that the diameter of the wire is 1.0 mm, we can calculate the radius (r) as 0.5 mm or 0.0005 m. The cross-sectional area can be determined using the formula A = π * r^2. Plugging in the values, we can find the resistance. Finally, we can substitute the resistance and the given current into Ohm's Law to find the potential difference, which is 32 V.

The peak voltage across the device can be calculated using the formula Vpeak = Vrms * √2, where Vrms is the root mean square voltage. In this case, the Vrms can be found by dividing the power (500 W) by the current (I) and then multiplying it by the voltage (120 V). So, Vrms = (500 W / I) * 120 V. Since the device is connected to a 120 V ac power source, the Vrms would be equal to 120 V. Therefore, the peak voltage would be 120 V * √2, which is approximately 170 V.

The resistance of the platinum wire increases as indium starts to melt because the temperature is increasing. This change in resistance can be attributed to the change in resistivity of the platinum wire with temperature. The temperature coefficient of resistivity for platinum is given as 3.9 * 10^(-3)/C°. By using the formula for resistance, R = ρ * L/A, where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area, we can calculate the change in temperature. The change in resistance is 3.072 Ω - 2.000 Ω = 1.072 Ω. By rearranging the formula, we can solve for the change in temperature, which is equal to the change in resistance divided by the temperature coefficient of resistivity multiplied by the initial resistance. This gives us (1.072 Ω) / (3.9 * 10^(-3)/C° * 2.000 Ω) = 137.9 °C. Therefore, the melting point of indium is approximately 137°C.

The current in the wire can be determined using Ohm's Law, which states that current (I) is equal to the charge (Q) passing through a conductor per unit time (t). In this case, the charge is given by the product of the number of electrons (3.0 * 10^15) and the charge of each electron (1.6 * 10^-19 C). The time is given as 4.0 s. Therefore, the total charge passing through the wire is (3.0 * 10^15) * (1.6 * 10^-19) C. Dividing this by the time (4.0 s), we get the current in amperes. Converting this to milliamperes by multiplying by 1000, we find that the current is 0.12 mA.

Silver has the lowest resistivity value among the given options. This means that silver offers the least resistance to the flow of electric current compared to gold, copper, and aluminum. Silver is known for its high electrical conductivity, making it an excellent choice for applications where low resistance is desired, such as in electrical wiring and circuitry.

When the owner shortens the Nichrome wire by 10%, the resistance of the wire decreases. According to Ohm's law (V = IR), if the resistance decreases, and the voltage remains constant, the current flowing through the wire will increase. Since power is calculated using the formula P = IV, an increase in current will result in an increase in power. Therefore, the power dissipated in the heating element will increase to 2.2 kW.

The current through a wire can be calculated using Ohm's law, which states that current (I) is equal to voltage (V) divided by resistance (R). The resistance of a wire can be calculated using the formula R = (resistivity * length) / cross-sectional area. In this case, the length of the wire is given as 10.0 m and the radius is given as 0.321 mm, so the cross-sectional area can be calculated using the formula A = π * r^2. Once the resistance is calculated, the current can be found by dividing the voltage (12.0 V) by the resistance. Using these calculations, the current through the wire is 0.388 A.

When a resistor is connected across a voltage source, the current flowing through the resistor can be calculated using Ohm's Law, which states that current (I) is equal to voltage (V) divided by resistance (R). In this case, the voltage is 220 V and the resistance is 4000 Ω. By substituting these values into the formula, we get I = 220 V / 4000 Ω = 0.055 A. Therefore, the correct answer is 0.055 A.

When the length of a wire is doubled, the resistance of the wire also doubles. However, when the radius of the wire is doubled, the resistance decreases by a factor of four. This is because resistance is inversely proportional to the cross-sectional area of the wire, which is determined by the square of the radius. Therefore, when both the length and radius are doubled, the resistance decreases by a factor of 2 (doubling the length) and increases by a factor of 4 (doubling the radius), resulting in a net decrease in resistance by a factor of 2. Thus, the resistance becomes half as large.

To calculate the cost of operating the soldering iron, we need to determine the energy consumed. The power of the soldering iron is given as 25 W, and it operates for 8.0 hours. So, the total energy consumed is 25 W * 8.0 hours = 200 Wh or 0.2 kWh. The cost of energy is given as $0.08/kWh. Multiplying the energy consumed (0.2 kWh) by the cost per kWh ($0.08), we find that the total cost of operating the soldering iron is $0.016.

When the current flowing through a circuit of constant resistance is doubled, the power dissipated by the circuit will quadruple. This is because power is directly proportional to the square of the current (P = I^2 * R), where P is power, I is current, and R is resistance. When the current is doubled, it becomes I * 2, so the power becomes (I * 2)^2 = 4 * I^2, which is four times the original power. Therefore, the power dissipated by the circuit will quadruple.