Current Electricity

Ohm’s law and it's Limitations, Resistivity and it's Temperature Dependency

  • Resistance depend up on current and potential difference.
  • Reciprocal of resistance is conductance \tt (G) = \frac{1}{R}
  • Unit of conductance is (ohm)−1.
  • Specific resistance \tt P = \frac{R A}{l}
  • Unit of specific resistance = Ohm.meter
  • Specific resistance is independent of dimensions.
  • Resistivity is specific property of a metal whereas resistance is a bulk property of conductor.
  • Silver, Copper and Aluminium have very low value of resistivity.
  • Fuse wire is made of tin-lead Alloy.
  • The elements of heating devices are made up of nichrome which has high resistivity and high melting point.
  • The filament of electric bulb is made up of tungsten which has low resistivity and low melting point.
  • Conductivity is the measure of the ability of a material to conduct electric current through it \tt \sigma = \frac{1}{\rho}
  • The current (i) through a conductor is proportional to potential difference (v) applied is Ohms law V = iR.
  • Ohms law is just an empirical relation not a universal law.
  • The substances which obey Ohm’s law are called ohmic devices.
  • All metals are ohmic devices.
  • The substances which donot obey Ohms law are called non ohmic substances.
  • Vacuum tube, diode and thermistor are non ohmic substances.


  • I-v Graph for ohmic devices 


  • I-v Graph for non ohmic devices


  • Slope of I-V Graph gives resistance \tt R = \frac{V}{I}
  • Variation of resistance with temp can be measured by temperature coefficient of resistance \tt \alpha = \frac{R_{t} - R_{0}}{R_{0} (t)}
  • Variation of resistivity with temperature \tt \alpha = \frac{\rho_{t}-\rho_{0}}{\rho_{0}t}
  • If "α" is positive then resistance of materials increases with temperature.
  • If "α" is negative then resistance of materials decreases with temperature.
  • When two wires are connected in series and Resistance does not change with temperature R1α1 = R2α2
  • Thermistor is a heat sensitive non ohmic device.
  • For a metals whose resistance is zero below certain temperature called critical temperature.
  • The materials in the critical temperature state are super conductors.
  • Joules heating effect work done W = i2Rt
  • Joules heat H = i2Rt = vit = \tt \frac{v^{2}}{R} t
  • Power consumed by the resistor P = vi = i2R = \tt\frac{v^{2}}{R}
  • Power consumed \tt P_{c} = \left[\frac{V_{Applied}}{V_{Rated}}\right]^{2} P_{R} (PR = power rated).
  • When VA > VR the bulb gets damaged.
  • When VA > VR power consumption will be lesser than rated power.
  • An electric bulb of low wattage will give more in series because its resistance is more than a high wattage bulb.
  • When resistances are connected in parallel. P1R1 = P2R2.
  • More power is consumed in smaller resistance in parallel combination.
  • 'n' equal resistors are connected in parallel PP = nP.
  • If the n cells are connected in series and parallel which the power dissipated in Pseries = \tt \frac{P}{n} and Pparallel = nP then the combination gives \tt \frac{P_{P}}{P_{S}} = n^{2}
  • 1 B.T.U = 1 K.W.H = 36 × 105 Joules.
  • \tt Units (KWH) = \frac{Number \ of \ watts \ \times \ Number \ of \ hours}{1000}

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1. Ohm's Law
If physical conditions of a conductor such as temperature remains unchanged, then the electric current (I) flowing through the conductor is directly proportional to the potential difference (V) applied across its ends.
    I ∝ V
or V  = IR

2. Electrical Resistance
The obstruction offered by any conductor in the path of flow of current is called its electrical resistance.
Electrical resistance, R = \frac{V}{I}

3. Resistivity
Resistivity of a material of a conductor is given by
\rho = \frac{m}{ne^{2}\tau}

4. Resistivity of metals increases with increase in temperature as
ρt = ρ0 (1 + αt)

5. Electrical Conductivity
The reciprocal of resistivity is called electrical conductivity.
Electrical conductivity \left(\sigma\right) = \frac{1}{\rho} = \frac{l}{RA} = \frac{ne^{2}\tau}{m}