Electric Circuits Legacy Problem #3 Guided Solution
Problem*
Determine the amount of time that the following devices would have to be used before 1.0x106 C (1 million Coulombs) of charge passes through them.
- LED night light (I=0.0042 A)
- Incandescent night light (I=0.068 A)
- 60-Watt incandescent light bulb (I=0.50 A)
- Large bathroom light fixture (I=2.0 A)
Audio Guided Solution
The electric current is the rate at which charge flows past a point on an electric circuit in a given amount of time. In equation form, it can be said that I is equal to Q divided by T, where I represents the current in amperes, where Q represents the quantity of charge flowing past the point in units of coulombs, and T represents the time over which this charge flows in units of seconds. Here in this question, we're given the current of various devices, and we're asked to find the time that it would take for 1,000,000, or 1 times 10 to the 6th, coulombs of charge to flow through that device. And so we need to take our equation I equal Q over T and rearrange it so that we can solve for time. That means you'll have to multiply both sides of the equation by T to get the T out of the denominator, and then you'll have to divide through by I to get T by itself, that giving you T equal Q over I, where the Q again is 1.0 times 10 to the 6th, and you simply need to divide that by the current in units of amperes. When you do, you'll get a time period in units of seconds, and if you wish, you can divide by 60 twice to convert to minutes, and then to hours, and then you can divide by 24 if you wish to convert to days, and if you wish, you can divide by 365.25 to convert to years. One of the answers that you see listed there should be the answer that you receive. And in all instances, it's rounded to two significant digits.
Solution
- 2.4x108 sec = 6.6x104 hr = 2.8x103 d = 7.5 yr
- 1.5x107 sec = 4.1x103 hr = 170 d
- 2.0x106 s = 560 hr = 23 d
- 5.0x105 s = 140 hr = 5.8 d
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.
Read About It!
Get more information on the topic of Electric Circuits at The Physics Classroom Tutorial.