Question 640088: If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the resistance, R. If the current is 180 milliamperes (mA) when the resistance is 5 ohms, find the current when the resistance is 15 ohms.
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! The formula you should use is
(1) V = IR , where V, in volts, is the voltage across the resistor whose resistance is R ohms. The voltage across the resistor causes a current I, in amps, to flow through the resistor.
Your problem statement specifies that I = 180 ma when R = 5 ohms.
Placing I and R into (1) yields
(2) V = (180/1000)*5, the reason for dividing by 1000 is to convert milliamps to amps.
Simplifying (2) yields
(3) V = 0.9 volts
Your problem statment also states that this voltage is held constant at 0.9 volts, while we change the resistance to 15 ohms; then find the new current, which we shall name as I'.
Substitute V = 0.9 and R = 15 into (1) yields
(4) 0.9 = I'*15 or
(5) I' = 0.9/15 or
(6) I' = 0.060 amps or multiplying by 1000 gives
(7) I' = 60 ma
Note that as stated, as the resistance increases, the current decreases. Mathematically stated, current is inversely proportional to the resistance.
This property can be shown by solving (1) for I.
(8) I = V/R,
where you can see arithmetally that if V is constant and the value of R is increased, the value of I decreases. In this case the resistance tripled from 5 ohms to 15 ohms and the current was reduced by a factor of three, from 180 ma to 60 ma. Thus the inverse change. Conversely, if R decreased, the current would increase. Physically this makes sense because resistance, by its very name, resists the flow of current and a larger resistance reduces the amount of current.
I apologize for blabbering about this property, being a Ph.D. in Electrical Engineer you hit my favorite topic. Thanks for asking.
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