Resistance

  • Resistance is the ratio of the potential difference across it to the current flowing through it.

R=VIR=\frac{V}{I}

R = Resistance, V = Voltage, I = Current

  • Resistance of a conductor depends on its length, its cross-sectional area, the material which it is made, and its temperature.

Resistance and Length

  • The resistance of a uniform conductor is directly proportional to its length.

R⠀α⠀lR⠀\alpha⠀l

for a fixed cross-sectional area A, R = Resistance, l = Length

Resistance and Cross-sectional Area

R⠀α⠀1AR⠀\alpha⠀\frac{1}{A}

for a fixed length l, R = resistance, A = Cross-sectional Area

SI Unit: ohm (Ω\Omega)

A conductor has a resistance of 1 ohm if the current through it is one ampere and when the potential difference across it is 1 voltage.

Ohm’s Law

For certain conductors at constant temperature current is directly proportional to the voltage.

I⠀α⠀VI⠀\alpha⠀V

I = Current, V = Voltage

If a conductor obeys Ohm’s Law resistance remains the same as the voltage and current vary.

Resistors in Series

R=R1+R2+R3R=R_1+R_2+R_3

Resistors in Parallel

1R=1R1+1R2+1R3\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}

Resistivity

ρ=RAl\rho=\frac{RA}{l}

ρ\rho = Resistivity, A = Cross-sectional Area, l = Length

SI Unit: ohm metre (Ω\Omega m)

Resistance changes linearly with temperature.

  • As the temperature of the metal increases, the metal atoms vibrate at a greater rate.

  • The electrons, in trying to move through the metal, collide more frequently with the atoms.

  • The electrons therefore meet increased resistance. i.e. the resistance of a metallic conductor increases as the temperature increases.

Variation of a Thermistor with Temperature

Resistance of the thermistor decreases dramatically as the temperature increases.

  • As the temperature of the thermistor increases, more electrons break free from their bonds.

  • There are thus more charge carriers available for conduction.

  • Thus the resistance decreases.

The Wheatstone Bridge

  • The Wheatstone Bridge is said to be balanced when the Galavanometer reads zero.

When the Wheatestone Bridge is balanced:R1R2=R3R4\frac{R_1}{R_2}=\frac{R_3}{R_4}

Metre Bridge

When the bridge is balanced: R1R2=∣AB∣∣BC∣\frac{R_1}{R_2}=\frac{\left\vert AB\right\vert}{\left\vert BC\right\vert}

Potential Divider Circuit

  • If two resistors are conncected in series across a fixed voltage supply:

  • The greater voltage is across the greater resistor.

  • The sum of the voltages is the suply voltage.

  • The resistors divide the potential difference of the supply in the ratio of their resistances.

Variable Potential Divider Circuit

  • Provices any voltage from zero volts to the supply voltage by sliding a movable contact.

  • As the movable contact is moved from A to B the output voltage increases from zero volts (at A) to 12 volts (at B)