S-Cool Revision Summary

S-Cool Revision Summary

Resistance, Ohm's Law and Conductance

The more resistance there is the more energy that is needed to push the same number of electrons through part of the circuit.

Resistance is measured in ohms, Ω, and the resistance of a component can be found using an ohmmeter.

Resistance can be calculated using the equation:

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Where:

R = resistance (ohms, Ω)

V = potential difference (volts, V)

I = current (amps, A)

For certain components, such as metal resistors at a constant temperature, the resistance, R, doesn't change. These components obey Ohm's Law.

Ohm's Law states that the current through a metallic conductor is proportional to the potential difference across it if the temperature remains constant.

Any resistor that obeys Ohm's Law is called an ohmic resistor. Any resistor that doesn't do this is cleverly called a non-ohmic resistor.

Conductance

Conductance, G, is the opposite of resistance, and tells us how easy it is for a current to flow through something. Conductance is measured in siemens, S.

1 S = 1 ohm-1

Conductance can be calculated using the equation:

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Where:

G = conductance (siemens, S)

I = current (amps, A)

V = potential difference(volts, V)

R = resistance (ohms, Ω)

Voltage-Current Graph for a Metal Conductor

When metals are heated it causes the atoms in the metal to vibrate more.

Imagine an electron in a current travelling through heated copper. It's trying to flow through the metal but the atoms are vibrating more, so they are going to get in the way more, causing more collisions. More collisions gives more resistance. We say the atoms have a larger collision cross section.

So increasing temperature of a wire leads to increasing resistance (and of course a decrease in conductance).

That means that the higher the current passing through a wire the greater its resistance will become. So most resistors don't obey Ohm's Law unless the temperature is kept constant.

Current-Voltage Graph for a Diode

Diodes behave like ohmic resistors when the current is travelling through them in the correct direction. However, if the current is reversed the resistance of the diode is extremely high.

Thermistors and Light-dependent Resistors

Some devices, made from semiconductors, break the rule we've just explained (typical) and reduce their resistance as temperature increases. This is because the extra energy makes the atoms release electrons, allowing them to move more easily, this in turn reduces the resistance.

These devices are called thermistors. These are often used in temperature controls.

Light-dependent resistors conduct better when light falls on them and releases more electrons.

Combinations of Resistors

If you have more than one resistor in a circuit it is often useful to be able to calculate the total resistance of the combination.

In series: RT = R1 + R2 + R3

In parallel: Copyright S-cool

Resistivity

What factors affect the resistance of a material?

  1. Length - the further electrons have to travel through material, the more collisions they will have so the higher the value of resistance.
  2. Area - a bigger area means that in any 1 second more electrons will be able to travel through a piece of wire. More electrons means more current which means less resistance.
  3. Material - if you swapped all the copper wire in a circuit for wood you'd notice a lot less current and a lot more resistance in the circuit. The ability of a material to conduct is called its resistivity, p. Resistivity is measured in ohm-metres (Ωm).
  4. Temperature - but we've covered that in 'current-voltage graphs'.

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Conductivity

As conductance is the reverse of resistance, so conductivity is the reverse of resistivity.

So conductivity, Copyright S-cool

Conductivity is measured in Sm-1

EMF and Potential Difference

In any circuit there are components that put energy in to the circuit and components that take energy out. From now on, we will say that any device putting energy into a circuit is providing an electo-motive force (emf) and any device taking it out has a potential difference (pd) across it.

Both emf and pd are measured in volts, V, as they describe how much energy is put in or taken out per coulomb of charge passing through that section of the circuit.

The best way to think of them is:

Emf - is the amount of energy of any form that is changed into electrical energy per coulomb of charge.

pd - is the amount of electrical energy that is changed into other forms of energy per coulomb of charge.

Internal Resistance

Where is the heat energy coming from?

It's from the current moving through the inside of the cell. The resistance inside the cell turns some of the electrical energy it produced to heat energy as the electrons move through it.

Therefore, inside the cell, energy is put into the circuit by the cell (the emf) but some of this energy is changed into heat by the internal resistor (a pd).

So the pd available to the rest of the circuit (the external circuit, as some questions may refer to it) is the emf voltage minus the pd lost inside the cell:

V = E - Ir

Where:

V = pd across the external circuit (V)

E = emf of the cell (V)

I = current through the cell (A)

r = value of the internal resistance

(Ir = the p.d. across the internal resistor)

Note: V is sometimes called the terminal pd as it is the pd across the terminals of the cell

High and Low Voltage Power Supplies

Power supplies delivering low voltages and higher currents, like a car battery, need to have a low internal resistance, as shown above. High-voltage power supplies that produce thousands of volts must have an extremely high internal resistance to limit the current that would flow if there was an accidental short-circuit.

Finding Internal Resistance Experimentally

As V = E - Ir, if you plot a graph of terminal pd, V, against current, I, the gradient of the graph will be equal to the internal resistance of the cell.

If there is more than one cell in series the internal resistances of the cells must be added.

Equations

Resistance

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Emf, E = I (R + r) - for the internal resistance, r, of a cell.

Symbols

Resistance

R = resistance, Ω

V = potential difference, V

I = current, A

ρ = resistivity, Ωm

l = length, m

A = area, m2

r = internal resistance of a power source, Ω