How is breathing affected if the smooth muscle of the bronchial tree relaxes

This leads to dilation of the walls of the respiratory lower respiratory tracts. Thus maximum volume of air is conducted (inhaled) through these tracts to reach the lungs with each inspiration. The rate of diffusion of oxygen across the bronchi walls also increases with the dilation; with consequent increases in perfusion pressure of oxygen with Hb in the blood.

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Explanation:

During the relaxation of the smooth muscles of the bronchial tree, there is dilatation of the airways to allow passage of air on inspiration, into the lungs.

Bronchodilation decreases the resistance of the respiratory airways and increases the lung capacity resulting the maximum volume of air being conducted into the lungs. This also results in increased oxygen diffusion and perfusion of the blood.

During inspiration, the smooth muscles of the bronchioles are relaxed. The lungs expand and the diaphragm flattens out to accommodate the lungs. The volume of the thoracic cavity increases to take in more air.