Electric Circuits Legacy Problem #7 Guided Solution
Problem*
A coffee cup immersion heater utilizes a heating coil with a resistance of 8.5 Ω. Determine the current through the coil when operated at 110 V.
Audio Guided Solution
One of the most common equations in electric circuits is the equation that the electric potential difference, or voltage drop, delta V, is equal to the current, I, multiplied by the resistance, R. That's delta V equals I times R. And here in this problem, what we have is a coffee cup immersion heater that is plugged into a 110 volt outlet, and that would be the delta V in that equation. We're told that it has a resistance of 8.5 ohms, that's the R, and what we wish to solve for is the current. So if we plug those two numerical values into our equation, we can do a little algebra and solve for current, and it ends up being the delta V divided by the R, and it would come out to be 12.9412 volts per ohms, where a volt per ohm is the same thing as an ampere or an amp. We can round that to two significant digits such that the answer is 13A or 13 amperes.
Solution
13 A
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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