Physics

Problem

A battery of emf

E

and internal resistance

r

is connected to an external resistor

R

. a. (i) Obtain an expression for the current in the circuit in terms of

E

R

and

r

. b. (ii) Show that the power delivered to the external resistor is

P = \frac{E^2 R}{(R + r)^2}

. c. (iii) Using calculus, determine the value of

R

for which this power is maximum. d. (iv) For

E = 12\,\text{V}

and

r = 1\,\Omega

, calculate the value of

R

that gives maximum power and find the corresponding power.