Resistances in Parallel :
When conductors are joined in parallel, following relations hold good
I = I1 + I2 + I3
1 / R= 1 / R1 + 1 / R2 + 1 / R3
R= ( R1 +R2 + R3 ) / ( R1R2 + R2R3 + R3R1 )
G = G1 + G2 + G3
Effect of Temperature on Resistance :
Resistance of all materials is affected by the variations in temperature. The effect of temperature in general is as follows:
(i) Resistance of most of the metallic conductors increases with rising temperature
(ii) Resistance of non-conductors or insulators usually decreases with rising temperature.
Temperature coefficient of resistance :
It is defined as the increase in resistance per ohm original resistance per
oC rise in temperature. Thus
α = (Rt - Ro )/(Ro . t)
where
Ro = resistance at 0 oC
Rt = resistance at t °C
t = temperature rise in oC
Usually
α is of the order of l0 -4 Ω/ Ω oC for most of the metals.
In case of insulators and electrolytes, α is usually negative.
Temperature coefficient of carbon is negative.
Resistor color coding :
Carbon resistors are physically small in size and color code is used to represent their value in ohms. The scheme is shown in Figure above. Various codes for colors are given in the table below :
| Color Code | |
| Color | Value |
| Black | 0 |
| Brown | 1 |
| Red | 2 |
| Orange | 3 |
| Yellow | 4 |
| Green | 5 |
| Blue | 6 |
| Violet | 7 |
| Grey | 8 |
| White | 9 |
DRIFT VELOCITY :
The drift velocity vd of charge carriers is related to current I by the equation
I = n α e vd
Where
n = density of charge carriers in conductor,
α = area of cross-section of conductor,
e = charge on each carrier.
A large amount of energy has to be supplied to pull an electron from inside to outside of the metal surface. This energy is called work function. This energy is the characteristic of the metal.
SUPER-CONDUCTIVITY :
As temperature of metallic conductor decreases, their resistivity decreases. In certain metallic conductors as temperature decreases, the resistivity falls to zero at a certain temperature called super-conducting temperature. It happens for mercury at 4 K and for tin at 3.72 K. This phenomenon is called super-conductivity.
Resistivity of semiconductors decreases with increase in temperature
ρT = ρo e-(Eg / kT)
where
Eg = band gap energy,
ρT = resistivity at T K,
k = Boltzman constant.
NON LINEAR DEVICES :
The devices for which potential difference V Vs current I curve is not a straight line are called non-linear devices. They do not obey Ohm's law and resistance of these devices is a function of V or I e.g. vacuum tubes, junction diodes, thermistors etc.
The dynamic resistance of such devices is given as
r = Lt∆ t → 0 ∆ V / ∆ I = d V / d I
where
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