Question Video: Determining the Overall Dimensions of One Quantity Divided by Another Physics

Video Transcript

Quantity 𝑎 has dimensions of 𝐼. Quantity 𝑏 has dimensions of 𝐼 times 𝑇 to the negative one. What are the dimensions of 𝑎 divided by 𝑏?

Here, we’re told that the dimension of quantity 𝑎 is 𝐼. We can assume that 𝐼 represents current. Quantity 𝑏 has dimensions 𝐼 times 𝑇 to the negative one. Here, 𝑇 we can assume is time. If we calculate 𝑎 divided by 𝑏, we want to know the dimensions of that fraction. This will be equal to the dimensions of 𝑎 divided by the dimensions of 𝑏. That’s equal to 𝐼 divided by 𝐼 times 𝑇 to the negative one.

Note that since we have dimensions of 𝐼 in both numerator and denominator, these dimensions cancel out. All that remains is one over 𝑇 to the negative one. If we multiply both numerator and denominator of this fraction by 𝑇, then in the denominator, 𝑇 times one over 𝑇 becomes one. So the fraction simplifies to time 𝑇. The dimensions of 𝑎 divided by 𝑏 are 𝑇.