A 12V source with internal resistance 0.25Ω is joined in series with a cell of unknown emf E and internal resistance 0.50Ω, together with an external resistor R. The current in the circuit is measured under two conditions:
Case I: The two sources aid each other (their positive terminals are in the same direction). The current is found to be 2.0A.
Case II: The unknown cell is reversed so that the sources oppose each other. The current is now 0.50A and flows from the 12V source towards the cell of emf E.
(i) Establish one equation connecting E, R and the given numerical data for Case I.
(ii) Establish a second independent equation for Case II.
(iii) Solve the two equations simultaneously to determine the unknown emf E and the external resistance R.