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# proportion

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In physics, Ohm's law says that current through a wire, I, is directly proportional to voltage, V, and inversely proportional to resistance, R:
I = V/R
It's also true that resistance is directly proportional to the length of the wire.  We have a piece of wire.  We pass 60 volts through this wire and measure 200 milliamps of current.  If I cut the wire in half and pass 400 volts through it, how many milliamps of current will I measure?

Jun 4, 2023

#1
0

i = v / r

and

r = L

200 = 60 / r

r = 10 / 3

cut wire in half means r = 10 / 6 or 5 / 3

i = 400 / 5 / 3

i = 240

Jun 5, 2023
#2
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I==V/R
R==V/I

200 milliamps ==200 / 1000 =0.2 amps.
R==60 / 0.2 ==300 ohms.
300 / 2 ==150 ohms - resistance in 1/2 of original wire.

I ==V/R
I==400 / 150 ==2.67 amps.
2.67 x 1,000 ==2,670 milliamps of current.

Jun 5, 2023
#3
+36654
+2

Cutting the wire in half will increase the amps by a factor of 2   to   400 ma         (because the resistiance is halved)

increasing the volatage ACROSS the wire will increase the amps by  400 / 60

400 / 60  *  400 ma = 2666.7 mAmps

(NOTE : Voltage is apllied ACROSS a component ....not THROUGH it)

(current goes THROUGH a componet)

Jun 5, 2023
#4
+2
+1

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JamesHutchings  Jun 6, 2023
edited by JamesHutchings  Jun 21, 2023