Electric Circuits Legacy Problem #13 Guided Solution
Problem*
The power of a 1.5-volt alkaline cell varies with the number of hours of operation. A brand-new D-cell can deliver as much as 13 A through a copper wire connected between terminals. Determine the power of a brand-new D-cell.
Audio Guided Solution
Alkaline cells, or a collection of cells, known as batteries, deliver energy to electrical circuits. The rate at which they deliver the energy to the electrical circuit is known as the power rating. And the power rating can be calculated from the knowledge of the current and the electric potential difference impressed across the circuit. Here, that electric potential difference impressed across the circuit is 1.5 volts. And the current through a wire, simply a wire with nothing else added to the circuit, is 13 amps. What we wish to do is calculate the power rating as I times V. When you do so, 13 times 1.5, you get 19.5 watts, which can be rounded to two significant digits as 20 decimal place watts.
Solution
20.0 W (rounded from 19.5 W)
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities and record them in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(\descriptive{\text{δV}}{δV,change in voltage} = 9.0\unit{\volt}\); \(\descriptive{R}{R,resistance} = 0.025\unit{\ohm}\); \(\descriptive{I}{I,current} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
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