Coursework To Find The Internal Resistance Of A PowerSupply

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Coursework To Find The Internal Resistance Of A Power Supply

The electrical supply on satellites needs to be kept at a constant voltage and the lost volts need to be taken into account when drawing different currents.

Aim

The aim of this investigation is to find the internal resistance of a power supply and to see if this value changes at five different voltage settings. Using a variable resistor to vary the load resistance at different voltage settings and obtaining both ampere and voltage readings and then plotting graphs of terminal potential difference against current to find the different values for the internal resistance of the power supply.

Theory

We can investigate the internal resistance of a power supply by setting up a circuit such as the one shown in figure 1. The voltmeter is connected in parallel to measure the potential difference across the power supply and the ammeter is connected in series to measure the flow of current.

We would connect the voltmeter across the terminals of the power supply. The variable resistor is used to vary the load resistance to gain a series of values for current and corresponding voltmeter readings. Given that the power supply supports ohms law, potential difference is proportional to current under constant physical conditions. Due to this relationship, a graph of current (amps) against terminal potential difference (volts) can be drawn which can be used to work out the internal resistance of the cell. This has been shown in figure 2.    

In figure 2, he power supply in the circuit is supplying a current (amps) to the external circuit. The internal resistance (r) of the power supply is constant provided that temperature of the equipment is constant. The current in the circuit increases as the load resistance is reduced, resulting in the terminal potential difference across the power supply to fall. In order to understand why there is a drop in terminal potential difference, we need to consider the idea of internal resistance. Any power supply will have internal resistance because of the material it is made from. This material (conductor), under normal circumstances will have resistance, also called internal resistance (r). The internal resistance of the power supply obeys Ohm’s law, which states that for an ohmic conductor the potential difference is proportional to current. Therefore as a current flows through the circuit, there is a drop in potential difference across the internal resistance, which is called the lost volts. The potential difference across the power supply is known called the terminal potential difference (Ir). From Kirchhoff’s second law we know that:

                                                   E = IR + Ir                                                 (1)

Where E is the Electromotive Force (EMF) of the power supply, maximum energy per unit charge that the power supply can deliver.

R is the external (load) resistance.

And I is the current flowing through the circuit.    

We know that:

V = IR

This equation can be substituted into equation (1) to give us the equation:

EMF = terminal potential difference + lost volts

E = V – Ir                                                       (2)  

Using this equation, we know that the internal resistance of the power supply is constant. As the current flowing through the power supply increases, the lost volts will increase. If the current decreases, then the lost volts also decreases until the current is zero. At this point, the potential difference across the terminals of the power supply will be equal to its EMF. This can also be seen in figure (2).

We can plot a graph of current (amps) against potential difference (volts) using the voltage and current figures as the load resistance is increased. We can use equation (2) and rearrange it in the form y = mx + c:

V = E – Ir

V = -Ir + E

y = mx + c

Therefore the gradient (m) is the internal resistance,-r, and the y-intercept is the Electromotive Force (E).

Safety Precautions:

As we are using mains electricity, we must make sure that no water should come in contact with the equipment which could damage the circuit and cause the fuse to blow. The work surface will be cleared of clutter before beginning experiment to make sure that the equipment is stable. When connecting and disconnecting equipment, I will turn of the power pack to avoid electrocution.

Variables that could affect my experiment:

The temperature of the power pack will affect the results obtained. If the power pack were at a low temperature, then its internal resistance would be less compared to a warmer power pack where its internal resistance will be higher. The greater internal resistance occurs since the temperature of the power pack (the components inside the power pack that transforms the mains voltage) increases because in the metal components there are positive ions which collide with electrons that are flowing around the circuit. As a result the electrons loose energy. As the metal components temperature increases, the positive ions vibrate more and as a result there are more collisions and more resistance to motion. In order to maintain the same, constant, temperature of the power pack, it will be switched on to take the results and then switched off. I will use direct current in my experiment and as a result, the voltage being delivered by the power supply will fluctuate slightly and therefore a completely accurate reading from the voltmeter will not be able to be taken. In my calculations, I assumed that there is negligible resistance in the wires of the circuit, but this could increase if the power supply was switched on continuously for a long period of time.  

Measurements and Readings That Will Be Taken:

I will measure the length of the metal rail and split the length into eight different sections. Readings of voltage and current will be taken from the voltmeter and ammeter.

Which Variables Will Be Changed and Which Kept Constant:

The variable resistor will be used to change load resistance in the circuit by moving the sliding contact along in order to record several values of current and potential difference to enable me to find the internal resistance of the power supply. The internal resistance of the power supply will be kept constant by keeping its temperature constant through all tests; this will be achieved by turning on the power supply for a small period of time to take the voltage and ammeter reading and then switching it off again to let it cool. The load resistance will be increased uniformly by moving the contact in the potentiometer across 2cm seven times and therefore current readings will decrease. Therefore load resistance and as a result current in the circuit was varied. I did this by marking seven points along the bar of the variable resistor and I moved the variable resistor to each of these points, with my first reading starting from the end of the variable resistor. Figure 3 below illustrates how I did this:

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Prediction:

I predict that as the internal resistance of the power supply will increase as the voltage setting is increased and there will be a greater voltage drop across the power supply as the voltage setting in increased.  

Plan of Action:

Preliminary Experiment:

In my preliminary experiment I used the apparatus as shown on the next page in figure 4. I turned the power supply on, set at two volts and increased the load resistance by moving the bow contact further along ...

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