2. An external resistor with resistance R is connected to a battery that has emf & and internal resistance r. Let P be the electrical power output of the battery. By conservation of energy, P is equal to the power delivered to the external resistor. r ww E R www (a) Find P in terms of E, r, and R. (b) If E = 40 V and r = 22, calculate the power delivered to the external resistor for six different values of R: 0.25 N, 1 N, 1.75 N, 2.5, 3.25 N, and 4 . (c) In Part (b), you should have found that P does not increase monotonically as R increases. Using the equation for P from Part (a), find the value of R in terms of r such that P is maximized. What is the maximum value of P in terms of & and r?

2. An external resistor with resistance R is connected to a battery that has emf & and internal resistance r. Let P be the electrical power output of the battery. By conservation of energy, P is equal to the power delivered to the external resistor. r ww E R www (a) Find P in terms of E, r, and R. (b) If E = 40 V and r = 22, calculate the power delivered to the external resistor for six different values of R: 0.25 N, 1 N, 1.75 N, 2.5, 3.25 N, and 4 . (c) In Part (b), you should have found that P does not increase monotonically as R increases. Using the equation for P from Part (a), find the value of R in terms of r such that P is maximized. What is the maximum value of P in terms of & and r?