RESISTANCE

Ammeters

Should be connected in series with the circuit or part of the circuit, through which the current is to be measured. The positive terminal of the ammeter should be connected, directly or indirectly, to the positive terminal of the voltage source. An ammeter should have low resistance so as the current would not be affected in the circuit and accurate values would be obtained from the circuit.

If there is a break point in the series circuit

no current flows

Two or more resistors connected in series

offer a greater resistance to current flow than any one of the resistors

Use of variable resistors

- Volume controls on radios, television sets etc. - Speed controls on wind shield wipers - Light dimmers

Resistance of a conductor increases if:

1. Its length increases 2. Its diameter decreases 3. resistivity of a material i.e. good conductors have low resistance (metals) insulators have high resistivity (wood, wool etc.)

Two main advantages of parallel circuits

1. Same voltage across each component 2. If there is a break in the circuit the current can pass through another component.

How to investigate the current-potential difference relationship for different conductors?

1. Set up the circuit below. Device D may be metal wire, a filament lamp, a diode, a solution of copper sulphate etc. 2. Use the rheostat to vary the current and potential difference. Record several pairs of I/V readings for each device you test. 3. Draw a graph of I against V for each device. - The voltmeter is connected across the device - The ammeter is connected in series with the device - The rheostat allows both the current and the potential difference to be varied.

RT total resistance in series

R₁ + R₂ + R₃

Series circuit

A circuit in which all parts are connected end to end to provide a single path of current.

Rheostat

A rheostat or variable resistor is a two-terminal device. The resistance between the two terminals may be varied by sliding contact or other means.

Resistance

All components in an electric circuit provide a certain impediment to current flow. This property of circuit components is known as resistance. Resistance either limits the current flowing or produces heat or provides suitable potential drops.

Graph obtained if the device D

An example is an electrolytic cells, say of copper sulphate solution with copper electrodes. This system obeys Ohm's law, since the graph is a linear one.

Graph for an ohmic device

An example may be a length of resistance wire, or a colour coded or wire-wound resistor. For these types of devices the graph of current versus potential difference is a straight line which passes through the origin.

Ohmic devices

Devices which obey Ohm's law.

Two types of resistors

Fixed resistors and variable resistors

Parallel circuits (current, resistance, voltage/potential difference and power)

For the parallel arrangement of resistors: ~ The potential difference across each parallel branch or load resistor is the same and is equal to the potential difference of the battery; ~ The reciprocal of the total resistance equals the sum of the reciprocals of the individual resistances: 1/RT = 1/R₁ + 1/R₂ + 1/R₃ ~ The total current is the sum of the currents in the individual branches: IT = I₁ + I₂ + I₃ ~ The total current divides at each junction leading to parallel branches of a circuit in such a way that the potential difference across each resistor is the same. ~ The total resistance for a parallel combination of resistors is always less than the value of the smallest resistance; ~ The total power dissipated equals the sum of the powers dissipated in the individual resistors; ~ a break in any branch of a parallel circuit does not affect other branches. However, the total current decreases; ~ Adding an extra branch in parallel with those already present increases the total current taken from the cell or battery

Fixed resistors

Have one specific value for example 5 ohms or 1 million ohms

Current Law for Parallel Circuits

In the image meter, A₃ registers the current taken from the battery. Meter A₄ also registers the current taken from the battery. Reading on A₃ = reading on A₁ = [reading on A₁ + reading on A₂] This illustrates the current law for parallel arrangements which states that 'the sum of the currents entering a junction is equal to the sum of the currents leaving that junction'.

Graph for a semi-conductor diode

Non-ohmic device

S.I. unit for resistance

Ohm (Ω)

Resistance in parallel for two resistors

RT parallel = RₙRₙ/Rₙ + Rₙ

Determination of total resistance in series circuit

The total resistance of a series combination of resistors may be determined experimentally from the potential difference and the current: The total current dissipated in a series circuit is equal to the sum of the powers dissipated in the individual resistors. For the circuit in the image: I = VAD/R₁ + R₂ + R₃ Note that VAD is voltage A to D If the resistors R₁, R₂ and R₃ are replaced by a single resistor of value RT whose value is R₁ + R₂ + R₃, the same current I will be drawn from the battery and will flow through the circuit.

Graph for a lamp filament (non-ohmic)

This graph is an approximate straight line at low currents. The resistance of the lamp filament increases at high currents and the graph curves correspondingly. It gets hot and the particles within the lamp misbehave and does not conform to ohm's law.

Non-ohmic device

Those devices which do not obey Ohm's law

How to analyse combined series-parallel circuits

To solve problems on series-parallel circuits, follow these steps: 1. Redraw the circuit so that resistances are easily seen. 2. Reduce the circuit to a simple series (or equivalent) circuit in which parallel segments of the original circuit are replaced by equivalent series resistances. 3. Calculate the total resistance of the circuit. 4. Calculate the total current, etc. (in series)

Potential difference

V = I x R (Current x resistance)

Ohm's Law

V = I x R (current x resistance) At constant temperature, the potential difference across the ends of a conductor is directly proportional to the current through it.

Voltmeters

are used to measure the potential difference between two points in a circuit. The voltmeter should be connected in parallel. A voltmeter should have a high resistance so as to draw as little current as possible from the circuit and not develop its own voltage.

Variable resistors

either have a range of values or can be adjusted to the specific resistance required in a circuit.

Voltmeters placed separately across R1, R2 and R3

give different readings but, Vbattery = VAD = VR₁ + VR₂ + VR₃ = IR₁ + IR₂ + IR₃ or V₁ + V₂ + V₃

Resistors

special components the conduct electricity but make it difficult for electrons to flow through them. Resistors oppose, control or limit the current in electrical circuits.

Current in a series circuit

the same current flows through all components - in this case, through the three resistors. the battery and connecting wires; identical ammeters placed at A, B, C and D give the same reading