Power in Circuits Practice Problems

Batteries store energy that is used in diverse ways. The starter motor in a four-cylinder engine draws 130 A at 12 V. If the starting process lasts 2.5 s, determine the energy supplied. 

A device for administering electric shock operates at 1280V and delivers a current of 18.8 mA creating a painful shock on the target. A pulse lasts 50.0 milliseconds. Determine the power and energy delivered to the target per pulse if the current is constant.

Your household is connected to a 240 V power line. Your 13A plug fuse blows, and you replace it with the readily available 5A fuse. You connect your 75W TV and 500 W fridge through the fuse. Determine the rating of a washing machine that will blow the fuse when added to the circuit.

An electric kettle is rated at 1200 W when operating at 220 V.  Determine the resistance of the electric kettle at these operating conditions.

An electrical device runs using power supplied by two 12.0 V batteries connected in series. The resistance of the device is measured to be 5.40 Ω. If the device is used for 1 day, determine the total energy it takes from the batteries.  

A vehicle has two 12.0 V batteries connected in series. The combined batteries drive a starter motor of resistance 5.40 Ω. If the batteries are ideal, determine the power supplied to the motor.

A portable electric drill uses an 18.0 V battery. The battery stores 3.24 × 10⁵ J of electrical energy and can sustain the drill for 15 minutes for each full charge. Determine the average current supplied to the drill during operation.

An electrical circuit with two power sources is connected as shown. Determine the power at which electrical energy is converted to other energy forms in the 6.0 V power supply.

A group of students make the circuit shown below. Determine the combined rate at which the 4.0-Ω and 7.0-Ω resistors convert electrical energy into heat. 

A section of the circuit of an electrical appliance is shown below. Determine the power supplied by the 13.5 V power supply.

An electric device of "R" resistance is connected to an ideal battery with a potential difference of 1.2 V and consumes an electric power current of 0.0835 W. Determine the power current consumed by the device when it is connected to a different ideal battery with a charge of 12.0 V, assuming that "R" remains constant throughout the changes in the power current consumption.

You are provided with the circuit below. Prove that the power supplied by the 13.0 V cell is equal to the total power dissipated in the other components of the circuit.

There are two options to choose from: investing in a $10.00 compact fluorescent bulb that lasts for 12,000 hours, or opting for a $1.00 halogen bulb with a lifespan of 1,000 hours. The compact fluorescent bulb consumes 12 W, while the halogen bulb consumes 48 W. Considering an electricity cost of $0.12/kWh, what would be the total cost, including the initial purchase price and energy usage, to achieve 12,000 hours of illumination for each bulb? This evaluation is commonly known as a life-cycle cost analysis.

An electric generator produces a potential difference of 350 V. If the generator drives a current of 2.5 A for a duration of 2.3 s, calculate: i) the total energy generated during this time. ii) the total charge that flows through the generator.

Two light bulbs are connected and illuminated in the circuit depicted in the diagram. One bulb has a power rating of 75 W, while the other has a power rating of 100 W. Based on their wattages, which bulb should shine brighter?

In the FIGURE below, all six identical bulbs emit light. The battery used is perfect. What is the sequence of brightness for these bulbs, listed from the brightest to the least bright?

What is the length of a tungsten filament in a halogen lamp that operates at 100.0 V and 75.0 W, given that the filament has a high-temperature resistivity of 9.71 × 10^-8 Ωm and a diameter of 5.00 μm?

Consider a hospital that consumes 50,000 kWh of electrical energy monthly. Given that the supply voltage to the hospital is 230 V, calculate the average current flowing through the hospital's power line.

Consider a small manufacturing plant where the machines collectively consume 80 kWh of electrical energy daily. If the electrical supply to the plant operates at a voltage of 220 V, determine the total electrical resistance of the plant.

What is the comparison between the total power delivered to the resistors when they are connected in parallel and when they are connected in series in a circuit with resistors measuring 3.2 kΩ, 4.8 kΩ, and 6.4 kΩ, and a power supply of 120 V?

A square surface is placed in a uniform electric field as shown in the figure below. The electric flux through the surface is measured to be -7.0 N•m²/C. Determine the magnitude of the electric field.

A capacitor with a capacitance of 225 µF is initially charged using an 18.0 V battery. The capacitor is then connected to a 2.25 Ω resistor, by closing a switch, causing the energy to be discharged through the resistor. Determine the power dissipated in the resistor 125 µs after the switch is closed.

Given that a hairdryer functions at 240 V and utilizes a heating element made of a tungsten wire with dimensions 6.8 m length and 0.60 mm diameter, and considering the resistivity, density, and specific heat of tungsten as 5.6 × 10^-8 Ωm, 19300 kg/m³, and 134 J/kg•K respectively, what is the duration required for the heating element to warm from 25°C to 300°C(approximately the temperature at which it begins emitting heat waves), taking into account that 60% of the heat energy is lost to the surroundings?

In an electricity pricing system based on time-of-day, where rates vary between peak and off-peak hours, let's analyze a situation where the electricity cost is $0.21/kWh from 7:00 a.m. to 10:00 p.m. and $0.09/kWh at all other times. What will be the yearly expense for electricity if a 3.5 kW air conditioner operates daily from 4:00 a.m. to 8:00 p.m.?

An LED light with a power rate of 10 W and operating voltage of 20 V is connected to a battery providing 30 V of electricity. Find out the resistance value of a series resistor that allows the LED to operate safely.

Determine the battery voltage for the circuit shown in the figure if the 25-Ω resistor dissipates 1.2 W of power.

A small bulb is connected across a 9.0 V battery with some wires. The current in the wire is 0.75 A. Calculate the energy the battery will lose in 2 minutes.

A hairdryer requires 200 V to produce 1.5 kW of heat. Calculate the resistance of the dryer's heating element.

How bright will a 60-W lamp designed for 230 V be if an electrician connects it to a 115 V outlet, compared to a 60-W 115-V lamp? Assume brightness is proportional to power consumed.

Sarah leaves her 40-W desk lamp on all year. With electricity costing $0.15/kWh, how much will it add to her annual bill?

How much less power is lost if a solar farm transmits 800 kW of power at 60,000 V instead of 15,000 V to a distribution center through the cables with a total resistance of 2.5 Ω?

An engineer designs a 1.8-meter-long stainless steel wire to function as a heating element reaching 2600 K when a current of 22 A passes through it. If the wire loses energy only through radiation (emissivity 𝜀=0.6) and the surrounding temperature is 20°C, what should be the diameter of the wire?

An electric water heater operates at 2.0 horsepower on a 220 V supply. What is the average current drawn by the heater? (Hint: 1 hp = 746 W)

You are tasked with designing a solar-powered boat with a powerful 60-kW motor. To ensure the motor operates efficiently, the battery system for the ship is configured to provide a constant voltage of 400 V. Assume there are no energy losses in the transfer of power from the battery to the motor. What is the current that the motor needs to draw from the battery?

Imagine that you are working on a kitchen laboratory project involving a 3000-W electric kettle that is connected to a 220-V power source. Using this kettle, you need to bring 200 mL of water, which is currently at 20°C, to a temperature of 90°C. However, the kettle is only 70% efficient. How long will it take for the kettle to heat the water to the desired temperature? The specific heat capacity of water is 4.186 J/g°C.

An electric heater that is rated at 75 W operates at 110 V. When the temperature is cold at 20°C, its resistance is 10 Ω. After a few moments of operation, when the temperature is hot, its resistance will increase to 140 Ω.

(a) Determine the power the heater consumes immediately after turning it on, when the temperature becomes cold.

(b) Calculate the power consumption once the heater has reached its operating temperature, when it reaches a hot temperature.

Determine the current flowing through the resistors P and Q if resistor P is rated at 240 V and 60 W for industrial use, while resistor Q is rated at 24 V and 60 W for electronic devices.

Determine the resistance of each heating element if a heating element X, which is used in kitchen appliances, is rated at 220 V and 120 W while a heating element Y, which is designed for small electronic devices, is rated at 110 V and 120 W.

A student uses a 2.0 kW washing machine for 1.5 hours/day, three 50 W LEDs for 7.0 hours/day, a 3.2-kW dryer for 1.0 hours/day, and various other electronics the power of which amounts to 2.2 kWh/day. Given that per kWh of electricity costs $0.13, determine the monthly electricity bill for 30 days for this particular student.

A washing machine motor operates at 750 W. Given that its efficiency is 65%, calculate its power input.

The power output of a hairdryer is 1200 W, and its efficiency is 80%. Given that the voltage source the dryer is connected to is 110 V, calculate the input current it operates on.

An electric kettle is connected across a 110-V DC source. Given that it is operating at 1000-W, calculate its resistance.

What must be the rate of coolant flow that is required to flow through a 220 V electric motor that is drawing 18.0 A of current in order to ensure that the temperature does not rise and exceed 4.5°C?

An electrical heating coil is at a temperature of 250 K. It is operating at 100 W of power and is connected across a 120-V power source. Calculate its resistance.

How much power is lost in 30.0 m of aluminum wire with a diameter of 0.200 cm, used by an electrician to connect devices running at 230 V and drawing a total of 1500 W?

Suppose you're designing a cooking device that uses heating elements. Each heating element has a resistance 𝑅 and is rated for a certain voltage. You need to know how the power output changes if you connect 𝑛 identical heating elements in series versus in parallel, given that the same voltage V is applied in both cases.

In a laboratory, a resistor is connected to a power supply. The power supply voltage varies by 20% as it changes from 5 V to 6 V. Given that the resistor's resistance remains constant, calculate by what percentage the power delivered to the resistor varies.

The air inside of a greenhouse that has a volume of 80 m³ must be kept at a constant temperature of 25°C. For this reason, an electrical heating system is installed. The air is replaced three times every hour, and the initial air temperature is 10°C as it enters the greenhouse. The rate of heat loss through the glass walls is 900 kcal/h. Calculate the minimum wattage that the heater must have. (Assume that the specific heat of the air is about 0.15 kcal/kg°C and the density of the air is 1.3 kg/m³.)

A new LED light bulb design operates at an efficiency that is related to its operating temperature. If an older LED model operates at 3100 K and a newer model at 3300 K, Determine (i) the percent increase in efficiency of the newer model over the older one. (ii) At what wattage can the newer model produce the same results as a 50 W older model LED?