Physics

Problem

Two batteries are connected in series opposition with an external resistor

R

in a single closed loop. The first battery has emf

E_1

and internal resistance

r_1

, while the second has emf

E_2

and internal resistance

r_2

. a. (i) Derive an expression for the loop current

I

in terms of

E_1, E_2, r_1, r_2

and

R

. Assume current flows from the positive terminal of the battery with emf

E_1

. b. (ii) Hence calculate the current when

E_1 = 12\,\text{V},\; E_2 = 4\,\text{V},\; r_1 = 0.3\,\Omega,\; r_2 = 0.2\,\Omega

and

R = 5.5\,\Omega

. State the direction of current with respect to the positive terminal of the

12\,\text{V}

battery.