Old Cell, New Cell

Use Kirchhoff's laws to show that the voltage across the lamp is $V = \dfrac{\varepsilon_1/r_1 + \varepsilon_2/r_2}{1/r_1 + 1/r_2 + 1/R}$.

Calculate the voltage across the lamp, the current in each cell, and the lamp current. State the direction of the current in the old cell and what this means.

Calculate the lamp's power with both cells, and with the new cell alone. A friend says 'the two cells push against each other and cancel out, so the lamp won't light'. Use your results to correct this and to explain why mixing old and new cells is poor practice.

The camper now fits three identical fresh cells, each with emf $1.50\ \text{V}$ and internal resistance $r = 0.300\ \Omega$, in parallel across the same $2.00\ \Omega$ lamp. Another friend says this will 'triple the current compared with one cell'. Calculate the actual ratio of lamp currents and use limiting cases ($r \ll R$ and $r \gg R$) to explain when the friend would be nearly right.