Resistors and Ohm's Law: Videos & Practice Problems

An aluminum cable used in a low voltage power line has seven 4.8 mm diameter strands and transmits 430 A of electric current. If the length of the wire is 1.3 km, determine the amount of energy lost as heat each day.

A heating element made of tungsten has a resistance of 40.0 Ω at 600°C. Determine its resistance when the temperature is 10°C.

A copper pipe is 5.0 m long. The outer diameter is 5.125 inches, while the inner diameter is 4.805 inches. What is the resistance of the pipe when measured i) along its length ii) along its wall thickness? Assumes each area acts like an equipotential surface.

 An aluminum solid wire has a diameter of 2.91 mm. Several wires are usually bundled to form a transmission cable. Determine the resistance of a 1.20 km long wire.

A rod has a resistance R. A craftsman fabricates the rod to create a new rod that has 4 times the length of the original rod. Assuming the new rod has the same density and resistivity, and all material is conserved, determine the rod's resistance in terms of R.

A 1.00 m long nichrome wire with a circular cross-section of diameter 0.800 mm is used for a resistance experiment. A constant current equal to 0.820 A flows through the wire at temperatures between 18°C and 75°C. Determine the greatest potential difference recorded over the entire length of the wire.

You are working on a circuit that requires an ammeter with a full-scale reading of 75.0 mA. However, the only ammeter available in the storeroom has a range from 0 μA to a full-scale reading of 300.0 μA. The resistance of the ammeter is measured to be 60.0 Ω. To achieve the desired 75.0 mA reading capacity, you consider adding a resistor in parallel to the ammeter. Calculate the effective resistance of the modified ammeter (which is a combination of the ammeter and the parallel resistor).

What is the percentage reduction in potential difference across a 15 Ω resistor when comparing an ideal battery to a battery with internal resistance?

Determine the optimal value for the resistance R of a load resistor connected to a 12-volt battery with an internal resistance of 2 Ω, in order to maximize the power dissipation by the load resistor.

Construct a circuit diagram (using proper symbols) for the circuit illustrated in the provided figure.

Determine the number of turns needed for a copper wire with a radius of 40 μm, coiled in a spiral around an insulating cylinder with a radius of 3.0 cm, to reach a resistance of 125 Ω.

An unknown long straight cylindrical metallic wire is connected to a 3.0 V battery. The wire has a radius of 3.0 mm and a length of 4.0 m. Using a Tesla meter, the magnetic field at a distance of 4.0 mm from the surface of the wire is measured to be 34 mT. Determine the resistivity of the wire.

Calculate the rate of charge flow when a 4.5 V battery supplies a current of 0.25 A.

A 3.0 m long wire with a radius of 1.0 mm is made of a material with a conductivity of 6.2 x 10⁷ Ω^-1m^-1. A current of 2.5 A flows through the wire. Determine i) the wire's conductance and ii) the potential drop across the wire.

A wire with a radius of 2.0 mm is subjected to an electric field of magnitude 1.6 x 10  ^-5 V/m. As a result, a current of 7.1 mA flows through the wire. Identify the material composing the wire.

In an electric circuit, a gold wire with a radius of 20 μm is used to precisely carry a current of 200 mA when connected to a 3.8 V power supply. Determine the length of wire needed to meet this condition. The resistivity of gold is approximately 2.4 x 10 ^-8 Ω•m.

The figure below illustrates the current versus voltage difference relationship for an unknown resistor. Determine the resistance of the resistor.

A thermistor has a resistance that varies with temperature according to the equation R(T) = R  ₀ e^{[C ((1/T) - (1/298 K))]}. Here, R₀ is the thermistor resistance at 298 K, T is the temperature in Kelvin, and C is a constant with units of Kelvin. The thermistor is connected to a 12.0 V battery. At a temperature of 25.0°C, the current flowing through the thermistor is 3.50 mA. When the temperature of the thermistor increases to 40.0°C, the current flowing through it increases by 10%. Determine the constant C.

Consider a 0.50 m copper pipe with an inner radius measuring 1.5 cm and an outer radius measuring 2.0 cm. A 15 A current flows radially, moving from the interior surface to the exterior surface of the pipe. Calculate the magnitude of the electric field at a distance of 1.5 cm and 1.8 cm from the central axis of the pipe.

A silver wire with a radius of 0.10 mm and a length of 1.50 m is connected to the terminals of a 4.5 V ideal battery. The electrical resistivity of silver increases with temperature and follows the relationship ρ = 1.59 × 10 ^-3 Ω•m [1 + 0.0038 °C ^-1 (T - 20 °C)]. Calculate the current flowing through the wire at 25 °C.

A cerebrospinal fluid with a conductivity of 1.7 Ω^-1 m^-1 flows through a cylindrical pipe representing a segment of the neuron. The pipe has a radius of 0.5 mm. Calculate the resistance of a 5.0 cm long column of cerebrospinal fluid.

In an electrical circuit, a capacitor is connected in parallel with a resistor having a resistance of 200 Ω. As the capacitor discharges, the current flowing through the circuit decreases to 30% of its original value within a time period of 7.5 ms. What is the capacitance of the capacitor?

An engineer is designing a lightning rod to protect the equipment of a radio station. The lightning rod, made of copper and with a length of 3.0 m, is placed on an isolated surface at the top of the building. The upper end of the rod is tapered to form a sharp point and the lower end is connected to the Earth. Determine the minimum radius required for the rod if the maximum allowable potential difference between the top and bottom of the rod is 140 V. Assume that an average lightning bolt carries a current of 40 kA and can persist for durations up to 80 μs.

A student connects a 2.0 m long ohmic wire with a radius of 0.5 mm across the terminals of a 1.0 V ideal battery. The current flowing through the wire is 7.0 A. Determine the material of the wire.

A scientist conducting a research project employs a specialized device that utilizes two metallic probes inserted into a cylindrical tube filled with an electrolyte solution. The probes are spaced 7.5 cm apart, and the tube has a radius of 2.0 mm. During the experiment, a potential difference of 24 V is applied across the metallic probes, resulting in a current of 450 μA flowing through the electrolyte solution. Determine the resistivity of the electrolyte solution.

The 3.8 V battery of a smartphone experiences an increase in its internal resistance due to exposure to extreme temperatures. Consequently, the battery's efficiency decreases, resulting in a shorter life. The cell phone can be connected to an external power source to charge its internal battery. Assume that the smartphone battery and the external power source are connected to a 0.75 Ω resistor, as illustrated in the figure below. Determine the current that passes through the 0.75 Ω resistor if the switch is closed.

Composite materials with varying compositions exhibit resistance variations along their length, allowing for the creation of customizable resistance profiles. Let's consider a wire composed of a composite material aligned in the y-direction with a radius of 1.5 mm and a resistivity expressed as ρ(y) = (2.7 × 10 ^-4 Ω•m ) e^{[-(3.5 /m)• y]}, where y represents the distance from the lower end of the wire. Calculate the resistance of a 30.0 cm long wire.

In some electronic applications, the conductance of a wire, given by G=σA/L, is more useful than its resistance. If a copper wire has a length of 3.0 m and a diameter of 2.0 mm, what is its conductance? The conductivity of copper is approximately 5.96×10⁷  Ω^-1 m^-1.

A nearly ideal ammeter is used in the circuit shown. What is the potential difference across the cell terminals?

A circuit constructed from an ideal ammeter is shown below. What is the current through the 10.0 Ω resistor?

A circuit with an ideal ammeter is shown below. What is the ammeter reading?

The figure below shows a DC transmission line carrying a current of 3200 A and a resistance of 2.2×10⁻⁵ Ω per meter. Determine the potential difference between a pigeon's legs perched on this line if the spacing between the legs is 6.0 cm.

A copper cylindrical rod has a length of 10.0 cm and a diameter of 2.0 cm, with a resistivity of ρ = 1.7 × 10⁻⁸ Ω⋅m. Calculate the resistance of the rod for a current flowing along its length (parallel to its axis).

A rectangular rod that is made out of graphite is oriented along the x-axis, has a width of 2.0 cm, and a height of 2.0 cm. The length of the rod is 5.0 cm. Given that the resistivity of graphite is 1.4 × 10^-5 Ω⋅m, calculate the resistance when the current flows perpendicular to the rod's length along the vertical axis.

A cylindrical rod made of titanium has a radius of 2.0 cm and a length of 12.0 cm. The rod is oriented with its length along the z-axis. Given that the resistivity of titanium is 4.0 × 10^-7 Ω⋅m, determine the resistance of the rod when the current flows through it along the z-direction.

A physics student takes ten similar resistors and connects them in series across a 200-V DC power source. Assuming that the internal resistance of the power source is negligible, determine the voltage across each resistor.

A DC battery with an internal resistance of 1.2 Ω and an emf of 9.0 V is connected in series with a special LED of 470-Ω of resistance. What is the terminal voltage for this battery?

You are in an electronics lab and must measure currents up to 30 A. The only available device is a galvanometer with a 50 Ω internal resistance, which deflects fully at 60 μA. Your task is to modify this galvanometer to function as an ammeter that reads up to 30 A. How would you accomplish this task?

A 50 Ω LED is connected across a 15 V battery with an internal resistance of 2.0 Ω. What is the terminal voltage of the battery?

A special type of patio light produces 6.0 W of power regardless of the voltage source connected to it. Twelve such patio lights are connected in series to a 180 V DC source. Calculate the resistance of each light. [Assume that the internal resistance of the voltage source is negligible.]

Six resistors are connected in a parallel configuration to a 150-V battery by two wires with a total resistance of 1.2 Ω. Given that the current through each resistor is 180 mA, calculate the resistance of each resistor and the fraction of the total power wasted in the wires. [Assume that the internal resistance of the voltage source is zero.]

A technician is testing a circuit with a 3000-Ω resistor. What voltage should be applied to produce a current of 0.40 A?

A homeowner is installing an outdoor lighting system that requires a 25 meter run of No. 16 aluminum wire, that has a diameter of 1.291 mm and is designed to handle up to 10.0 A circuits. The lights will draw a 8.0 A current, and the homeowner is concerned about the energy efficiency of this particular wire. Can you help determine the voltage drop over this 25 meter distance? [Hint: the Resistivity of aluminum = 2.82 × 10⁻⁸ Ω$\cdot$m]

In a laboratory, a scientist is examining two copper wires w₁ and w₂. Both wires have an identical electrical resistance. However, w₂ is three times longer than w₁. The scientist is interested in determining how the diameter of w₂ compares to the diameter of w₁. What is the ratio of the diameter of w₂ to the diameter of w₁?

In a laboratory experiment, a physicist investigates the electrical properties of different metallic wires. The physicist has two wires, both made from various materials: aluminium and nickel. The physicist wants to determine if a 2.5-mm-diameter aluminium wire can have the same resistance as a nickel wire of the same length. What will be the final observation of the physicist? [The resistivity of aluminium = 2.82 × 10⁻⁸ Ω⋅m, The resistivity of nickel = 6.84 × 10⁻⁸ Ω⋅m]

A student is working on a small electrical circuit and plans to use a 7.2 meter aluminum wire that has a 2 mm diameter. Before proceeding, she needs to calculate the resistance of the wire in order to ensure that it will work for her particular circuit. Given that the resistivity of aluminum is 2.65 × 10⁻⁸ Ω⋅m, what is the resistance of this wire?

A toaster with a resistance of 25 Ω is connected across a 200 V DC source. Calculate the current and charge that passes through the toaster in 20 minutes.

Find the conductance, in units of siemens "S", of a component that has a current of 250 mA flowing through it when a voltage of 5 V is applied.

A 6.0 Ω resistor is connected across a 12.0-V source. Assuming direct current, calculate the number of electrons that pass through the resistor per minute. [Hint: The charge on an electron is 1.602 × 10^-19 C.]

A 4.50-kΩ heating element is made from graphite and platinum resistors connected in series. Determine the resistance values for both resistors at 0°C to ensure the total resistance remains constant with temperature changes. Hint: The temperature coefficient for graphite is -0.00080/C° and for platinum is 0.00392/C°.

2.5 A of current is passing through a light bulb connected across a 220 V DC source. Suddenly, the voltage falls by 10% while the resistance of the light bulb reduces by 12%. Calculate the changed current.

At 25 ^∘C, the resistance of an electric heater’s copper coil is 15 Ω, and when hot, it reaches 180 Ω. Calculate the temperature of the coil when it is hot, considering the impact of thermal expansion on the length and cross-sectional area of the coil. The thermal expansion coefficient for copper is approximately 16.5 x 10^-6/C^∘ and its temperature coefficient for the resistivity is 0.0039/C^∘.

What battery voltage is needed in order to achieve a 10 mA current inside of a germanium diode that is connected in series with a 500 Ω resistor?

A copper wire has an initial resistance of 8.0 Ω at a temperature of 15 °C. Upon heating to 2100 °C, its resistance increases to 70 Ω. Given that the thermal coefficient of expansion for copper is α_L = 16.5 ×10^-6 °C^-1 and the temperature coefficient of resistivity α_r = 0.0039 °C^-1, determine the percentage change in the resistance (i) solely due to thermal expansion and (ii) solely due to change in resistivity.

A physics student is conducting an experiment to compare the electrical resistance of gold and aluminum wires for a project. Given the resistivity of gold as 2.4 × 10^-8 Ω⋅m and aluminum as 2.8 × 10^-8 Ω⋅m, what is the ratio of the resistance of a gold wire to that of an aluminum wire, assuming they have identical dimensions?

An engineer is designing a new type of electrical cable using silver, which has a resistivity of 1.59 × 10^-8 Ω⋅m. If the cable has a diameter of 2.0 mm and needs to be 200 m long for a particular application, what is the resistance of this silver cable?

For a laboratory experiment, a student needs to use a gold wire that has a resistivity of 2.44 × 10^-8 Ω⋅m. If the required length of the wire is 100 m and its diameter is 1.0 mm, what would be the resistance of this gold wire?

In an electrical engineering lab, a student is using a Wheatstone bridge to measure the resistance of a sensor R_d. The known resistances R_a, R_b, and R_c as shown in the figure balance the Wheatstone bridge with the sensor resistance R_d if the switch K is closed. (i) Derive the expression for R_d in terms of the known resistances. (ii) Given that when R_a = 200 Ω, R_b = 150 Ω, and R_c = 100 Ω the ammeter indicates zero current flow with the switch K closed, what should the value of R_d be in that case?

A conical section of a copper pipe gradually widens from one end to the other, forming a truncated cone shape as shown. The diameter at the narrow end of the pipe is D₁, while at the wider end, it is D₂. The total length of this conical section along its central axis is L. The pipe material has a resistivity ρ.

Determine the electrical resistance, R, between the two ends of the pipe in terms of D₁, D₂, L, and ρ. Assume that the current flows uniformly through each cross-section of the pipe, and that the widening of the cone is gradual, meaning (D₂ - D₁) ≪ L.

In an industrial setting, a robotic arm connected to a workstation through a control unit experiences a malfunction where the motor shorts out to its metal base, which is no longer grounded. An operator, in contact with the workstation, forms a complete circuit, allowing current to flow through the operator to the ground. In this setup, the motor has a resistance of 8 kΩ and is connected to a 220 V power supply. The resistance through the workstation is 8 kΩ, and the operator’s body has a resistance of 8 kΩ. The control unit has a very low resistance (assumed negligible). Calculate the current flowing through the operator.

The figure below shows the forward V-I characteristics of a germanium diode. Based on the curve, plot the graph of resistance R as a function of the current I for the diode when V > 0.

To determine the resistance of an unknown resistor, a student applies a series of potential differences V across it and measures the resulting currents I. Across the resistor, the following potential differences V (in volts) and corresponding currents I (in mA) are recorded. Plot V vs. I. Based on this plot, can Ohm’s law be concluded for the resistor? If so, calculate the resistance R of the resistor.

In a circuit designed with a zener diode voltage regulator, a stable voltage is needed across a load resistor. The circuit includes an input power supply voltage V_supply, a series resistor R_s = 2.80 kΩ, and a zener diode with a breakdown voltage of V_zener = 130 V and a maximum current rating of I_{zener max} = 120 mA. The load resistor, R_load = 18.0 kΩ, requires a stable output voltage of V_output = 130 V across it. Determine the range of supply voltages V_supply that will keep the output voltage regulated at 130 V. Assume that at the minimum supply voltage, there is no current through the zener diode, while at the maximum supply voltage, the zener diode reaches its maximum current of I_{zener max} = 120 mA.

In an electrical circuit experiment, a 11.0 V battery is connected to a combination of resistors arranged as shown below: R₁=23Ω, R₂=12Ω, R₃=4.8Ω, R₄=6.4Ω. The circuit includes a triangular network of resistors (R₂, R₃, R₄) with R₁ connected in series.

(a) Calculate the equivalent resistance of the circuit.

(b) Determine the current through 4.8Ω resistor (R₃).

(c) Find the current through 23Ω resistor (R₁).

(d) Calculate the power dissipation in 6.4Ω resistor (R₄).