And so then for the 75 waffle I have I? I'm gonna call this I to people 75 over B, this is 75 watts. So what? I knows if I'm keeping the voltage the same, I am going to have I to greater than I because I have a larger number in the numerator here. So I have I two is greater than I, or the 75 watt bulb is going to draw more current than the 60 waffle.
In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics. In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.
Click 'Join' if it's correct. Anthony G. Physics Mechanics 3 months ago. View Full Video Already have an account? Brianna O. Answer A 60 W light bulb and a Discussion You must be signed in to discuss. Video Transcript Well, let's say I have to light bulbs. Upgrade today to get a personal Numerade Expert Educator answer! Ask unlimited questions. Test yourself. Join Study Groups. Create your own study plan. Join live cram sessions. Live student success coach. University of Michigan - Ann Arbor.
Liev B. Numerade Educator. Marshall S. University of Washington. Zachary M. Hope College. Which draws more current?
Which uses the most energy? Can you tell from the color that the W filament is cooler? Is the brighter bulb a different color and if so why? Electric energy depends on both the voltage involved and the charge moved.
Power is the rate at which energy is moved, and so electric power is. Electric power P is simply the product of current times voltage. Power has familiar units of watts. Since the SI unit for potential energy PE is the joule, power has units of joules per second, or watts. For example, cars often have one or more auxiliary power outlets with which you can charge a cell phone or other electronic devices. Three expressions for electric power are listed together here for convenience:.
Note that the first equation is always valid, whereas the other two can be used only for resistors. In a simple circuit, with one voltage source and a single resistor, the power supplied by the voltage source and that dissipated by the resistor are identical. In more complicated circuits, P can be the power dissipated by a single device and not the total power in the circuit. Different insights can be gained from the three different expressions for electric power.
Thus, when the voltage is doubled to a W bulb, its power nearly quadruples to about W, burning it out. Then find the power dissipated by the car headlight in these examples, both when it is hot and when it is cold. The 30 W dissipated by the hot headlight is typical. But the W when cold is surprisingly higher. The current when the bulb is cold can be found several different ways. The cold current is remarkably higher than the steady-state value of 2. Most fuses and circuit breakers used to limit the current in a circuit are designed to tolerate very high currents briefly as a device comes on.
The more electric appliances you use and the longer they are left on, the higher your electric bill. This familiar fact is based on the relationship between energy and power. You pay for the energy used. For example, the more lightbulbs burning, the greater P used; the longer they are on, the greater t is.
It is easy to estimate the cost of operating electric appliances if you have some idea of their power consumption rate in watts or kilowatts, the time they are on in hours, and the cost per kilowatt-hour for your electric utility.
Kilowatt-hours, like all other specialized energy units such as food calories, can be converted to joules. The electrical energy E used can be reduced either by reducing the time of use or by reducing the power consumption of that appliance or fixture.
This will not only reduce the cost, but it will also result in a reduced impact on the environment. Improvements to lighting are some of the fastest ways to reduce the electrical energy used in a home or business. Fluorescent lights are about four times more efficient than incandescent lights—this is true for both the long tubes and the compact fluorescent lights CFL. See Figure 1 b.
Thus, a W incandescent bulb can be replaced by a W CFL, which has the same brightness and color. CFLs have a bent tube inside a globe or a spiral-shaped tube, all connected to a standard screw-in base that fits standard incandescent light sockets. Original problems with color, flicker, shape, and high initial investment for CFLs have been addressed in recent years. The heat transfer from these CFLs is less, and they last up to 10 times longer. The significance of an investment in such bulbs is addressed in the next example.
However, their cost is still high. If the cost of electricity in your area is 12 cents per kWh, what is the total cost capital plus operation of using a W incandescent bulb for hours the lifetime of that bulb if the bulb cost 25 cents? To find the operating cost, we first find the energy used in kilowatt-hours and then multiply by the cost per kilowatt-hour. The energy used in kilowatt-hours is found by entering the power and time into the expression for energy:.
Therefore, it is much cheaper to use the CFLs, even though the initial investment is higher. The increased cost of labor that a business must include for replacing the incandescent bulbs more often has not been figured in here.
Why do incandescent lightbulbs grow dim late in their lives, particularly just before their filaments break? Explain why there is no contradiction here. What is the power of a 1. What power is supplied to the starter motor of a large truck that draws A of current from a A charge of 4.
See Figure 2. Figure 2. The strip of solar cells just above the keys of this calculator convert light to electricity to supply its energy needs. How many watts does a flashlight that has 6. Find the power dissipated in each of these extension cords: a an extension cord having a 0. Electrons in an X-ray tube are accelerated through 1.
Calculate the power of the electron beam in this tube if it has a current of An electric water heater consumes 5. What is the cost of running it for one year if electricity costs See Figure 3. Figure 3.
On-demand electric hot water heater. Heat is supplied to water only when needed. What would be the maximum cost of a CFL such that the total cost investment plus operating would be the same for both CFL and incandescent W bulbs?
Calculate the cost for hours, as in the cost effectiveness of CFL example. Some makes of older cars have 6. Alkaline batteries have the advantage of putting out constant voltage until very nearly the end of their life. How long will an alkaline battery rated at 1. A cauterizer, used to stop bleeding in surgery, puts out 2. The average television is said to be on 6 hours per day. Estimate the yearly cost of electricity to operate million TVs, assuming their power consumption averages W and the cost of electricity averages
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