## 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 R
_{1}α_{1}= R_{2}α_{2} - 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 = i
^{2}Rt - Joules heat H = i
^{2}Rt = vit = \tt \frac{v^{2}}{R} t - Power consumed by the resistor P = vi = i
^{2}R = \tt\frac{v^{2}}{R} - Power consumed \tt P_{c} = \left[\frac{V_{Applied}}{V_{Rated}}\right]^{2} P_{R} (P
_{R}= power rated). - When V
_{A}> V_{R}the bulb gets damaged. - When V
_{A}> V_{R}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. P
_{1}R_{1}= P_{2}R_{2}. - More power is consumed in smaller resistance in parallel combination.
- 'n' equal resistors are connected in parallel P
_{P}= n_{P}. - If the n cells are connected in series and parallel which the power dissipated in P
_{series}= \tt \frac{P}{n} and P_{parallel}= n_{P}then the combination gives \tt \frac{P_{P}}{P_{S}} = n^{2} - 1 B.T.U = 1 K.W.H = 36 × 10
^{5}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

ρ_{t} = ρ_{0} (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}