HNRS 21W Lecture 10: Lecture 10

Show that, for linear demand (p = a – bq), per unit consumer surplus (consumer surplus divided by quantity sold) equals 0.5p/η where η is price elasticity.

Electric circuit consists of battery (with emf ε), resistor R and capacitor with initial capacitance C0, all connected in series as shown on the picture. The system has been connected as shown for some time, when suddenly, the capacitance is instantaneously changed to a value C=C0/η, η>1. Find: a) Current I(t) in the circuit as a function of time t after the change has been made (t=0 corresponds to the moment of change) b) the amount of heat Q that was dissipated in the resistor after the change has been made.

The velocity v of blood that flows in a blood vessel with radius R and length l at a distance r from the central axis is

where P is the pressure difference between the ends of the vessel and η is the viscosity of the blood. Find the average velocity (with respect to r) over the interval 0 ≤ r ≤ R. Compare the average velocity with the maximum velocity.