The plant will not likely increase its respiration rate during photosyntheis. Photosynthesis is when the plant build up energyn supply. These follwong elements will have an influence on the respiration rate during photosynthesis:
temperature - increase in temperature leads to an increase in respiration
moisture in the soil/medium
health status of the plant
age of the plant - young plants undergo higher respiration rates than older plants
During the day (the light period) photosynthesis under favorable conditions typically proceeds at a rate 5X - 10X that of respiration. Always remember that that if respiration rate exceeds photosynthesis rate for an extended period the plant will stop growing and slowly decline and die.