### Video Transcript

In an electric circuit, the current intensity ๐ผ going through a resistor varies directly with the voltage drop ๐ across the resistor and inversely with the resistance ๐
. Given that the current intensity is 2.5 amps with a voltage drop of five volts across a resistor of resistance two ohms, find the value of the current intensity when the voltage drop is 15 volts and the resistance is three ohms.

So to solve this problem, what we could use is the triangle here weโve got, which is one of our formula triangles. And itโs ๐ at the top, ๐ผ, and ๐
for voltage, current, and resistance. This is something that you come across in physics.

Well, actually, what I want to do first though, instead of straight away using the triangle, is to think about direct variation and inverse variation or direct proportion and inverse proportion. Well, if you take a look at what weโve got, weโre told that the current ๐ผ varies directly with the voltage and inversely with the resistance. So weโve got ๐ผ. And then weโve got our proportionality sign. Then weโve got ๐ over ๐
.

Well, what we can do is to start to form an equation. And we can do this using ๐พ, which is our proportionality or variation constant. Cause what we can say is that ๐ผ is equal to ๐พ multiplied by ๐ over ๐
. Well, the first thing we need to see is find ๐พ. And to do that, we can use the information weโve been given.

So weโre told that the current of intensity 2.5 amps with a voltage drop five volts across the resistor of resistance two ohms is what we get. So therefore, we can plug these values in to find out what ๐พ is. So when we do that, we get 2.5 is equal to ๐พ multiplied by five over two. So therefore, if we multiply both sides of the equation by two, we get five is equal to ๐พ multiplied by five. So therefore, weโre gonna get ๐พ is equal to one. And we get this because if we divide both sides by five, we just get ๐พ is equal to one. So what does this actually tell us?

Well, if we substitute back in our value of ๐พ to our equation, what weโre gonna get is ๐ผ is equal to one multiplied by ๐ over ๐
. Thatโs because our ๐พ is equal to one. Well, this can be rewritten as ๐ผ is equal to ๐ over ๐
. Well, great, cause if we check our triangle that we started with at the beginning, weโd see that this would also tell us that ๐ผ is equal to ๐ over ๐
. So it does look like itโs correct. And we can now use this to find the value of the current intensity when the voltage drop is 15 volts and the resistance is three ohms.

So to do that, what we do is we substitute in our values. So we get ๐ผ is equal to 15 over three. So therefore, what we get is ๐ผ is equal to five amps. So we know that the current intensity when the voltage drop is 15 volts and the resistance is three ohms is gonna be five amps. And we did that by showing how we could use the proportionality or variation constant to form an equation between ๐ผ, ๐, and ๐
. Which we then checked with our triangle that we know from physics, which tells us that ๐ผ is in fact equal to ๐ over ๐
.