Worksheet: Energy Dissipation by Conductors
In this worksheet, we will practice calculating the dissipation of energy by an electric circuit from its current, its resistance, and the voltage across it.
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?
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 . Assume a value of for the specific heat capacity of water.
What is the resistance of the resistor?
What is the voltage supplied by the power supply?
A physics student uses a 115 V immersion heater to heat grams of water for herbal tea in a cup. During the two minutes it takes to heat the water, the physics student becomes bored and decides to figure out the resistance of the heater. The student assumes that the water is initially at the temperature of the room, , and reaches a temperature of . Find the resistance of the heater. We now use a value of 4,180 J/kg⋅K for the specific heat capacity of water.
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 3,600 seconds. How much charge does the car’s battery move through its electric motor?
- A C
- B C
- C C
- D C
- E C
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 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 1,500.00-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?
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 Ω⋅m and a 7.0 cm2 cross-sectional area.
Find the loss of power in the transmission lines if power is transmitted at 200 kV (rms).
- A W
- B W
- C W
- D W
- E W
Find the loss of power in the transmission lines if power is transmitted at 25 kV (rms).
- A W
- B W
- C W
- D W
- E W
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 mm2. The charge carrier density of the copper in the wire .
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?
- A s
- B s
- C s
- D s
- E s
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?
What is the current through the resistor?
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 . A current is supplied to the resistor for 1,800 seconds. Assuming all the electrical energy dissipated by the resistor heats the water, find the final temperature of the water. Use a value of 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.
A baby’s feeding bottle consists of 57.0 g of glass and 2,330 g of baby formula. The bottle rests on a 15.0 V electric heater consisting of 2,112 g of aluminum. The heater increases the temperature of the aluminum, glass, and baby formula from to in a time interval of 300 s. In modeling the electric heating process, use a value of for the specific heat capacity of aluminum, for that of glass, and for that of the baby formula.
How much charge is moved through the heater during the heating process?
- A 5,700 C
- B 4,530 C
- C 1,680 C
- D 7,150 C
- E 7,120 C
What is the flow of electrons per second in the heater during the heating process?
- A electrons/second
- B electrons/second
- C electrons/second
- D electrons/second
- E electrons/second
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 and that the short circuit persists for 0.0700 s before a circuit breaker disconnects the circuit.