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How does the carbon cycle relate to photosynthesis and respiration?

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Hint: Carbon cycle is a way of re- using the atoms of carbon which are present in the atmosphere and they are taken from the living organisms like plants, algae, bacteria and animals and are released back to the atmosphere. This unending cycle of taking carbon atoms from the atmosphere and releasing them back is known as the “Carbon Cycle”. Plants are a major contributor to this carbon cycle.

Complete answer:
Carbon cycle is a process in which various living organisms take the carbon atoms in a specific form, for example, $C{O_2}$ for plants and this carbon is released back into the atmosphere by the means of living or non- living forms.
Carbon is an important element which is essential to lead life. Plants, algae, and bacteria are some organisms which use carbon as carbon dioxide to make food by the help of a process called “Photosynthesis”.
In photosynthesis, the plants use solar energy, carbon dioxide, and water to synthesize carbohydrates through various cycles. This process takes place in chlorophylls which are present in leaves.
This process helps in processing the bicarbonate or carbon dioxide atoms into organic molecules. Organic molecules are used by the organisms to make out other processes like cellular respiration, movement and locomotion, etc.
During this cellular respiration, the organic molecules or carbohydrates, processed by photosynthesis, are used and are acted upon by oxygen atoms.
There are multiple food chain reactions through which this organic molecule and oxygen atoms are converted into carbon dioxide again.
These reactions also take place inside animals and this process is carried out mostly in absence of light in plants. This process expels out the taken carbon dioxide from nature or atmosphere and hence the cycle completes.
Carbon is also released by the factory's emission and dead decaying matter.
Carbon from decaying matter in soil contributes to the formation of fossil fuel and this is how the cycle of carbon goes on and is connected with plant respiration and photosynthesis.

Note: The carbon cycle, as like other cycles, is very important for survival of life. A little disruption in the cycle might result in various consequences. For instance, plants make food with the help of carbon dioxide.
If carbon dioxide gets eroded from earth, plants will die, resulting in the death of animals and most other living organisms as we all use oxygen to breathe which is a by- product of photosynthesis.
Hence, a little bit of disruption in the cycle might result in the extinction of life on Earth.