Electric Circuits Legacy Problem #2 Guided Solution
Problem*
The large window air conditioner in Anita Breeze's room draws 11 amps of current. The unit runs for 8.0 hours during the course of a day. Determine the quantity of charge that passes through Anita's window AC during these 8.0 hours.
Audio Guided Solution
Current is the rate at which charge moves past a point on an electric circuit. In equation form, we can say I equal Q divided by T, where I represents the current, Q represents the quantity of charge flowing past the point, and time represents the time period over which that quantity of charge was measured. Here in this equation, we clearly have the current, 11 amps. We know that because they listed as current, and also from the unit. And we also have the time. What we wish to calculate is the quantity of charge. So we need to take our equation I equal Q over T and rearrange it to Q equal I times T. We can substitute 11 amps into the equation, and then we'll have to substitute the time, but it'll have to be done in units of seconds. After all, an ampere is the same thing as a coulomb per second. So we'll have to multiply an ampere or coulomb per second by a time in units of seconds. So taking the 8 hours, we can convert it to seconds by multiplying by 60 to get the minutes, and by 60 again to get the seconds. Then we'll take our time, which would end up being 28,800 seconds, and we'll multiply that by our 11 amps of current. That will give us the quantity of charge in units of coulombs. It would be 3.168 times 10 to the fifth, and we can round that to two significant digits.
Solution
3.2x105 C
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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