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In this lesson, we will learn how to calculate the dissipation of energy by an electric circuit from its current, its resistance, and the voltage across it.

Q1:

A resistor has a resistance of 1 . 0 × 1 0 2 Ω and dissipates electrical energy at a rate of 2.0 W.

What is the current through the resistor?

What is the voltage drop across the resistor?

Q2:

What is the maximum voltage that can be safely applied to a 15 kΩ resistor that has a 10 W power rating?

Q3:

A 30-V battery is used to supply current to a 10-kΩ resistor.

What is the power dissipated by the resistor?

Q4:

Consider a power plant located 25 km outside a town delivering 50 MW of power to the town. The transmission lines are made of aluminum cables with a resistivity of 2 . 6 5 × 1 0 − 8 Ω⋅m and a 7.0 cm^{2} cross-sectional area.

Find the loss of power in the transmission lines if power is transmitted at 200 kV (rms).

Find the loss of power in the transmission lines if power is transmitted at 25 kV (rms).

Q5:

A baby’s feeding bottle consists of 57.0 g of glass and 2 3 3 0 g of baby formula. The bottle rests on a 15.0 V electric heater consisting of 2 1 1 2 g of aluminum. The heater increases the temperature of the aluminum, glass, and baby formula from 2 2 . 0 ∘ C to 9 5 . 0 ∘ C in a time interval of 300 s. In modeling the electric heating process, use a value of 9 0 0 / ⋅ J k g C ∘ for the specific heat capacity of aluminum, 8 4 0 / ⋅ J k g C ∘ for that of glass, and 4 1 8 6 / ⋅ J k g C ∘ for that of the baby formula.

How much charge is moved through the heater during the heating process?

What is the flow of electrons per second in the heater during the heating process?

Q6:

A 420 V AC supply is short-circuited by a conductor of resistance of 0.850 Ω.

How much power is dissipated in the short circuit?

What is the current in the conductor?

Q7:

A resistor of an unknown resistance is placed in an insulated container filled with 0.75 kg of water. A voltage source is connected in series with the resistor producing a current of 1.2 A through the resistor that is maintained for 10.0 minutes, producing a water temperature increase of 1 0 ∘ C . Assume a value of 4 1 8 0 / ⋅ J k g C ∘ for the specific heat capacity of water.

What is the resistance of the resistor?

What is the voltage supplied by the power supply?

Q8:

The voltage across a resistor of resistance 0.010 kΩ is measured to be 4.00 V. What is the power dissipated by the resistor?

Q9:

In the circuit shown, the voltage source supplies 120 V, the resistance 𝑅 1 is 0.800 Ω, and the bulb is rated at 75.0 W.

What power will the bulb dissipate if 15.0 A passes through the wire when the motor is turned on?

What is the power of the motor?

Q10:

A battery-operated car that has a mass of 750 kg is powered by a 12.0-V battery. The car accelerates from rest to 25.0 m/s, climbs a hill with a height of 200 m, and finally travels at a constant 25.0 m/s while exerting a force of 500 N for 3 6 0 0 seconds. How much charge does the car’s battery move through its electric motor?

Q11:

What is the average power output of a heart defibrillator that dissipates 530 J of energy in 11.2 ms?

Q12:

A heart defibrillator produces a current of 10.0 A in a patient’s torso for 5.00 ms in an attempt to restore a normal heartbeat. 500 J of energy was supplied by the defibrillator.

How much charge was passed through the patient?

What voltage was applied to the charge that passed through the patient?

What was the resistance of the path taken by the charge that passed through the patient?

Q13:

A physics student uses a 115.00-V immersion heater to heat 400.00 grams (almost two cups) of water for herbal tea. During the two minutes it takes the water to heat, the physics student becomes bored and decides to figure out the resistance of the heater. The student starts with the assumption that the water is initially at the temperature of the room and reaches . The specific heat of the water is . What is the resistance of the heater?

Q14:

The short circuit of a 160 V appliance occurs in a cord that has a 0.700 Ω resistance. Calculate the temperature rise of the 5.00 g of matter around the cord, assuming the matter has an average specific heat capacity of 0 . 3 0 0 / ⋅ c a l g C ∘ and that the short circuit persists for 0.0700 s before a circuit breaker disconnects the circuit.

Q15:

A power plant that is located 6 . 0 × 1 0 4 m from a town transmits electrical power through copper wires of cross-sectional area 42.40 mm^{2} and resistivity of 1 . 6 8 × 1 0 − 8 Ω⋅m. The power is transmitted by a 100.0 A current. How much power is dissipated during transmission?

Q16:

A 190 V AC short circuit through a conductor generates a peak power of 84 kW.

What is the resistance of the conductor?

What would the average power be if the voltage were 140 V AC?

Q17:

Electrical power generators are sometimes tested by supplying a current to a large vat of water. A similar method can be used to test the heat output of a resistor. A resistor with a resistance of 20 Ω is connected to a battery with a terminal voltage of 12.0 volts. The resistor’s connecting leads are waterproofed, and the resistor is placed in a water bath containing 3.0 kg of water at a water temperature of 2 5 ∘ C . A current is supplied to the resistor for 1800 seconds. Assuming all the electrical energy dissipated by the resistor heats the water, find the final temperature of the water. Use a value of 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water and assume that the change in the water temperature causes a negligible change in the resistor’s resistance.

Q18:

A car battery of emf 16 V is used to power a lamp that has a power rating of 13.00 W and a voltage rating of 16.00 V when the lamp is taken on a camping trip. The battery is connected to the lamp by a cable of length 1.50 m containing 14-gauge copper wire of cross-sectional area 2.1 mm^{2}. The charge carrier density of the copper in the wire 𝑛 = 9 . 5 0 × 1 0 2 8 − 3 m .

How much current does the lamp draw from the battery?

What is the average time taken for an electron to pass through the connecting cable?

Q19:

A current of 25 A is drawn from a 1 . 0 × 1 0 2 -V battery for 30 seconds. By how much is the chemical energy of the battery reduced?

Q20:

A student uses a 100-W, 115-V radiant heater to heat his dorm room, between 6:00 pm and 7:00 am.

What current does the heater operate at?

How many electrons move through the heater?

What is the resistance of the heater?

How much heat was added to the dorm room?

Q21:

A resistor has a resistance of 120 Ω and a power rating of 0.200 W. The resistor is used in a circuit that initially supplies to it the maximum current that will not damage the resistor, 𝐼 m a x . If the current supplied is reduced to 0.250 𝐼 m a x , what is the power dissipated by the resistor?

Q22:

A 75 watt incandescent light bulb produces 900 lumens of light. Assuming an electricity price of $0.22 per kilowatt-hour, what is the annual cost of keeping the light bulb on for exactly eight hours a day?

Q23:

A resistor of resistance 30.00 Ω has a power rating of 2.50 W. The resistor is connected to a power supply with an output voltage set to produce in the resistor the maximum current that it can safely carry.

What output voltage is the power supply set to?

Q24:

A battery with an emf of 24.00 V delivers a constant current of 2.00 mA to an appliance.

How much work does the battery do in 180 seconds?

Q25:

A 120-V immersion heater consists of a coil of wire that is placed in a cup to boil the water. The heater can boil one cup of 2 0 . 0 0 ∘ C water in 180.00 seconds. A student buys one to use in their dorm room, but they are worried that they will overload the circuit and trip the 15.00-A, 120-V circuit breaker, which supplies the dorm room. In the dorm room, there are four 100.00-W incandescent lamps and a 1 5 0 0 . 0 0 -W space heater.

What is the power rating of the immersion heater?

What will be the total current in the circuit connecting the room if the immersion heater is turned on?

What will be the total current in the circuit connecting the room if the incandescent light bulbs are replaced with 18.00-W bulbs?

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