WEBVTT
00:00:00.970 --> 00:00:05.500
The current in a circuit varies inversely with the circuitโs resistance, measured in ohms.
00:00:06.040 --> 00:00:09.360
When the current is 40 amperes, the resistance is 10 ohms.
00:00:09.950 --> 00:00:12.310
Find the current if the resistance is 12 ohms.
00:00:12.650 --> 00:00:15.710
Round your answer to two decimal places if necessary.
00:00:17.120 --> 00:00:23.640
So the current in a circuit varies inversely with the circuitโs resistance, measured in ohms.
00:00:24.470 --> 00:00:26.640
Well, first, letโs define a couple of variables.
00:00:27.740 --> 00:00:36.640
Now, you can choose any letters you like, but Iโm gonna let ๐ผ be the current in amperes, and Iโm gonna let ๐
be the resistance in ohms.
00:00:38.050 --> 00:00:56.360
So if the current varies inversely with the resistance, it means that ๐ผ is directly proportional to one over ๐
or the current is equal to some constant โ letโs call it ๐ โ times one over ๐
, which we could just write as ๐ over ๐
.
00:00:57.640 --> 00:01:05.970
Now, weโre told that when the current is 40 amperes, so when ๐ผ equals 40, then the resistance is 10 ohms.
00:01:06.050 --> 00:01:07.870
So ๐
equals ten.
00:01:08.710 --> 00:01:12.000
So letโs use this information to try to work out the value of ๐.
00:01:13.320 --> 00:01:19.060
We just express the relationship between the current and the resistance as ๐ผ is equal to ๐ over ๐
.
00:01:19.450 --> 00:01:24.350
Now when ๐ผ equals 40, we can replace ๐ผ with 40 in our equation.
00:01:24.590 --> 00:01:29.700
And when ๐
is ten, we can replace ๐
with ten in our equation.
00:01:30.030 --> 00:01:37.090
Now if I multiply both sides by ten, I find out that 400 is equal to ๐ or ๐ is equal to 400.
00:01:37.430 --> 00:01:44.910
So I can now plug this back into my original equation and say that ๐ผ is equal to 400 over ๐
.
00:01:45.280 --> 00:01:48.830
And I can use that equation to work out the answer to the final bit of the question.
00:01:50.380 --> 00:01:54.390
Find the current if the resistance is 12 ohms.
00:01:55.410 --> 00:01:58.930
That means find the value of ๐ผ when ๐
is equal to 12.
00:02:00.190 --> 00:02:03.290
Well, we said that ๐ผ is equal to 400 over ๐
.
00:02:03.590 --> 00:02:07.250
Now weโre saying ๐
equals 12; we can replace ๐
with 12 in our equation.
00:02:08.470 --> 00:02:11.120
So this means that ๐ผ is equal to 400 over 12.
00:02:11.470 --> 00:02:14.100
Well 400 and 12 are both divisible by four.
00:02:15.150 --> 00:02:19.960
400 divided by four is 100 and 12 divided by four is three.
00:02:20.210 --> 00:02:23.360
So this is 100 over three or 33 and a third.
00:02:24.480 --> 00:02:26.590
Now, a couple of things that we need to be aware of.
00:02:26.840 --> 00:02:31.620
The question said round your answer to two decimal places if necessary.
00:02:31.620 --> 00:02:39.820
So it doesnโt want us to give this exact answer of 33 and a third; it wants us to give our answer in decimal format to two decimal places.
00:02:40.230 --> 00:02:44.020
We also know that the current is measured in amperes.
00:02:44.020 --> 00:02:47.740
So the unit is amperes; itโs important to include those in our answer as well.
00:02:48.970 --> 00:02:53.840
Well, 33 and a third is 33.3333333 and so on.
00:02:54.350 --> 00:02:59.880
So if we round that to two decimal places, thatโs just going to be 33.33.
00:03:00.150 --> 00:03:03.910
The next digit is only a three, so that last three wonโt round up.
00:03:05.460 --> 00:03:10.980
So our answer then is 33.33 amperes, correct to two decimal places.