A voltmeter is connected at X, with a movable probe C, such that the voltmeter is able to read the potential difference across the wire at different points between X and Y.
(b)
Sketch a graph on the set of axes below which shows how the potential difference V varies between X and Y as the sliding contact C moves from X to Y.
The Maximum Power Transfer theorem says the maximum amount of electrical power is dissipated in a load resistance RL when it is exactly equal to the internal resistance of the power source r.
The circuit below is used to investigate maximum power transfer.
A variable resistor, which acts as the load resistance RL, is connected to a power source of e.m.f. and internal resistance r, along with a switch S and an ammeter and voltmeter.
The graph below shows the results obtained for the power P dissipated in RL as the potential difference V across RL is varied:
(a)
Assuming the Maximum Power Theorem is valid, use the graph to determine the internal resistance of the power source.
The diagram shows a circuit which can be used to 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. ε = 0.5 V, is connected to an oscilloscope:
The chart below represents the trace shown on the oscilloscope screen when both of the switches S1 and S2 are open:
The y-gain of the oscilloscope is set at 1.5 V div–1.
(a)
Discuss what happens to the trace shown on the oscilloscope screen when switch S1 is closed.
Calculate the internal resistance of the battery if the vertical distance between the traces in part (a) and part (b) is measured to be half a division.
Determine the current in the cell that would move the trace shown on the oscilloscope screen back to its original position as shown in part a. Assume both switches, S1 and S2, remain closed.
Understanding the properties of e.m.f. and internal resistance can help the design decisions of architects and electrical engineers.
In an experiment to investigate power dissipation across two lamps, L1 and L2, an engineer connects them in a series circuit to a cell of e.m.f. 45 V and internal resistance 7 Ω.
The lamp L1 has a resistance of 10 Ω and L2 has a resistance of 25 Ω.
(a)
Calculate the percentage difference between the power generated by the cell and the power dissipated in the two lamps L1 and L2. Suggest a reason for this percentage difference.
The engineer wishes to maximise the power dissipated across each lamp and explores various alternatives to the circuit shown in part a.
(b)
Suggest and explain, using appropriate calculations, how the engineer should arrange the lamps L1 and L2 such that the power dissipated in each lamp is maximised.
The engineer comes up with a theoretical problem, which involves arranging a large number of identical lamps in parallel with each other, as illustrated below:
The lamps are connected to a cell of e.m.f. ε and internal resistance r.
(c)
Discuss the effect on the terminal p.d. supplied by the cell, and hence on the lamps, as more lamps are added in parallel.
