Hi! That's an awesome project, I'm curious to know what happens!
My guess is that the three main types of vitamin C you'll be able to buy at a drug store or grocery store are
powdered,
liquid, and
gel capsules.
If you get powder, you can dissolve some in water to make it liquid and thus easier to apply. If you get the vitamin C gel capsules, you can use a pin to puncture a capsule, then just squeeze it to get the vitamin C out.
How many carrots do you have? If you have enough, you could try a few different concentrations of the powdered vitamin C. This seems like the best approach to me. You can decide how to do it exactly once you have all the materials, but here's an example set-up: fill 4 glasses with the same volume of water. Add 0, 2, 4, or 6 tablespoons of powdered vitamin C and stir until totally dissolved (Note: depending on the volume of water you choose, this may be too much vitamin C and it might not all dissolve! You'll have to figure out an appropriate amount to use). Next, apply the dissolved vitamin C to each carrot (I'm not sure what tools you have, but you could use an eyedropper, a spoon, a small brush, etc. for this step). Ideally, you'd have both a normal carrot and infected carrot where nothing is applied. Then you'd have your 0% vitamin C solution (water), and apply it to one normal carrot and one infected carrot. Then you'd apply each of your more concentrated vitamin C solutions to both a normal carrot and an infected carrot. That covers all necessary controls. In a perfect world, you'd have multiple carrots (≥ 3) per test condition, but this may be asking too much!
Two final notes- the chemical name for vitamin C is ascorbic acid, and some products will have it labeled this way instead of using the common name, so keep an eye out! Also, a lot of products will say "vitamin C" but will also contain other ingredients. Make sure whatever you get is pure vitamin C so your experiment has the cleanest results!
Let me know if anything was unclear or if you have more questions! Good luck!
Megan