1.1. Figure 1 shows a circuit which can be used to find investigate the internal resistance r of a power supply. In this case, a battery consisting of six dry cells in series, each of e.m.f. $\epsilon$ = 0.5 V, is connected to an oscilloscope:   

Figure 1a

Figure 1b represents the trace shown on the oscilloscope screen when both of the switches ${S}_{1}$ and ${S}_{1}$ are open:

Figure 1b

The vertical sensitivity of the oscilloscope is set at 1.5 V div^–1. 

With reference to Figure 1b, discuss what happens to the trace shown on the oscilloscope screen when switch ${S}_{1}$ is closed.  

1.2. Use Figure 1b to draw the trace on the oscilloscope screen when both switches ${S}_{1}$ and ${S}_{2}$ are closed. 

Explain your answer.

1.3. Calculate the internal resistance of the battery if the vertical distance between the traces in part (b) and part (c) is measured to be half a division. 

1.4. Determine the current in the cell that would move the trace shown on the oscilloscope screen back to its original position shown in Figure 1b. 

Assume both switches ${S}_{1}$ and ${S}_{2}$ remain closed.