90PSC401_SE
Rationale:
In electricity, the potential difference (voltage) across an electrical circuit
facilitates the flow of electrons from the negative terminal to positive terminal.
Conversely, resistance is the opposition to the flow of electrons, and is measured
in ohms (Ω). The rate at which charge flows (current) between two terminals, can
be expressed as a ratio of voltage to resistance…
Such can be transposed to yield R…
This is Ohm’s law.
The resistance of a component in an electrical circuit, can be proportionally
affected by two variables: its length; the longer the length, the greater the
distance that collisions occur between delocalised electrons, and its cross-
sectional area, as a smaller cross-section reduces the quantity of electrons that
can travel at a particular point.
The tendency for the resistance of a component to be proportionally affected by
such factors, is its resistivity, and is an intensive property that identifies a
material. Observing that resistance is inversely proportional to cross-sectional
area, and is directly proportional to length…
1
R∝ , R ∝l
A
…the relationship between resistivity, and resistance to the factors that affect it,
can be summarised by the equation below…
R
ρ=
l
A
Because resistance increases proportionally with length of the resistor, by
quantifying the change in resistance (via. Ohm’s law) vs. change in length, such
can be inserted into the equation above, with a known and constant cross-
sectional area, to yield the resistivity and identity of a resistor.
Research Question:
By quantifying the relationship between resistance and length of an unknown
resistor, what is its resistivity, when the resistor is of constant cross-sectional
area and temperature?
Original Method:
The original experiment, ‘Investigating Ohm’s Law,’ from Grade 9 Oxford
Science, quantified the resistance of a known resistor, as a relationship between
voltage drop and current across a simple circuit. (Silvester, 2021)
, 90PSC401_SE
Modifications to the methodology:
The experiment was extended by…
- Introducing a potentiometer (figure 1) into the circuit, to function as the
unknown resistor and measure independent variable (length).
- Attaching a moveable crocodile clip (figure 1) to the potentiometer to
change the independent variable.
- Trialling five consecutive lengths of resistor (0.1m, 0.2m, 0.3m, 0.4m,
0.5m) - ensuring that sufficient data was collected to accurately yield
resistivity of resistor.
- Introducing two multimeters into the circuit (figure 1) - one in series to
measure current, one in parallel to the resistor to measure voltage drop,
to simultaneously yield measurements required to calculate resistance.
- Controlling and measuring diameter of potentiometer, as the
proportionality constant between length and resistance is the only
unknown variable being deduced.
The experiment was refined by…
- Controlling temperature as a variable of resistance, by immediately
switching off circuit after taking measurements. Increases validity of
experiment, by ensuring that any change in resistance measured, is solely
from experimental manipulation of length. Increases validity, as the
experiment will yield a closer result to the expected resistivity at room
temperature.
- Measuring five different voltages (2V – 10V) for every length tested.
Increasing sample space of data reduces the effect of random errors -
ensuring that the experiment is more reliable, and results are more
precise.
- Setting the multimeters at appropriate sensitivities to reduce
measurement uncertainty and increase reliability of measured voltage and
current.
Figure 1: Experimental setup.
Rationale:
In electricity, the potential difference (voltage) across an electrical circuit
facilitates the flow of electrons from the negative terminal to positive terminal.
Conversely, resistance is the opposition to the flow of electrons, and is measured
in ohms (Ω). The rate at which charge flows (current) between two terminals, can
be expressed as a ratio of voltage to resistance…
Such can be transposed to yield R…
This is Ohm’s law.
The resistance of a component in an electrical circuit, can be proportionally
affected by two variables: its length; the longer the length, the greater the
distance that collisions occur between delocalised electrons, and its cross-
sectional area, as a smaller cross-section reduces the quantity of electrons that
can travel at a particular point.
The tendency for the resistance of a component to be proportionally affected by
such factors, is its resistivity, and is an intensive property that identifies a
material. Observing that resistance is inversely proportional to cross-sectional
area, and is directly proportional to length…
1
R∝ , R ∝l
A
…the relationship between resistivity, and resistance to the factors that affect it,
can be summarised by the equation below…
R
ρ=
l
A
Because resistance increases proportionally with length of the resistor, by
quantifying the change in resistance (via. Ohm’s law) vs. change in length, such
can be inserted into the equation above, with a known and constant cross-
sectional area, to yield the resistivity and identity of a resistor.
Research Question:
By quantifying the relationship between resistance and length of an unknown
resistor, what is its resistivity, when the resistor is of constant cross-sectional
area and temperature?
Original Method:
The original experiment, ‘Investigating Ohm’s Law,’ from Grade 9 Oxford
Science, quantified the resistance of a known resistor, as a relationship between
voltage drop and current across a simple circuit. (Silvester, 2021)
, 90PSC401_SE
Modifications to the methodology:
The experiment was extended by…
- Introducing a potentiometer (figure 1) into the circuit, to function as the
unknown resistor and measure independent variable (length).
- Attaching a moveable crocodile clip (figure 1) to the potentiometer to
change the independent variable.
- Trialling five consecutive lengths of resistor (0.1m, 0.2m, 0.3m, 0.4m,
0.5m) - ensuring that sufficient data was collected to accurately yield
resistivity of resistor.
- Introducing two multimeters into the circuit (figure 1) - one in series to
measure current, one in parallel to the resistor to measure voltage drop,
to simultaneously yield measurements required to calculate resistance.
- Controlling and measuring diameter of potentiometer, as the
proportionality constant between length and resistance is the only
unknown variable being deduced.
The experiment was refined by…
- Controlling temperature as a variable of resistance, by immediately
switching off circuit after taking measurements. Increases validity of
experiment, by ensuring that any change in resistance measured, is solely
from experimental manipulation of length. Increases validity, as the
experiment will yield a closer result to the expected resistivity at room
temperature.
- Measuring five different voltages (2V – 10V) for every length tested.
Increasing sample space of data reduces the effect of random errors -
ensuring that the experiment is more reliable, and results are more
precise.
- Setting the multimeters at appropriate sensitivities to reduce
measurement uncertainty and increase reliability of measured voltage and
current.
Figure 1: Experimental setup.
