Current electricity: Rate of change of charge is called current. Unit is ampere and is equal to 1 Coulomb/sec. Dimension of current is [A], hence the dimension of charge is also [AT]
Current carriers: In solid conductors electrons are charge carriers, in electrolytes there are ions, in gases also ions.
In a conductor electrons are loosely bound to the nucleus and hence are free to move, but within its physical boundaries. They do have some thermal velocity, but net velocities for electrons are zero as they move in haphazard way. When some potential difference is applied across the ends of conductor (with the help of battery or otherwise), electron start drifting towards +ve potential or higher potential. During this journey they collide with neighboring atoms and electrons and hence keep on loosing energy (thus producing heat), as permanent force is acting on electron (due to electric field set up by battery) they keep on moving in that specified direction and ultimately reach opposite (+ve) terminal of conductor.
Terms being used in current electricity:
Drift velocity (vd): Average velocity with which an electron is drifted towards the +ve end of conductor under the influence of external electric field, it is of order of 10-5 m/s
Relaxation time(t): Time lapsed between two successive collisions
Mean free path (l): Average distance between two successive collisions.
Let ‘A’ is the area of conducting cylinder and ‘L’ is its length. ‘n’ be the number of free electrons per unit volume of conductor
Total charge (free) available in the conductor is given by
Q = n A L e, dividing both sides by time
I = vd e n A [Q/t = I, & L/t = vd ]
Theory: If ‘V’ is the potential difference across the conductor of length L, an electric field is developed in it. (Contrary to statement that electrical field is ZERO in electrostatics) Due to this electrical field
E = V/L, Force starts acting on it. F = qE = eE (Here q = e)
hence acceleration starts acting on it, thus eV/L = ma ⇒a = (eV)/mL
Now due to this force electron drifts towards the positive side of the conductor. But is stopped by the presence of neighbouring atoms and electrons, hence it collides with them. As the electrical force is always pushing the electrons they start moving once gain.
Now applying the first equation of motion between two successive collisions
v = u + at
we get vd = (eV)/mL ×τ
Equating both vd
we get usually called Ohm Law
Ohm’s Law: Physical conditions, like temperature mechanical strain etc. remaining constant current (I) is proportional to potential difference (V) across the conductor mathematically V = IR, where R is the resistance of conductor. Any conductor following Ohm’s law is also called linear conductor as the graph of V Vs. I is a straight line. Slope of this graph gives resistance.
Resistance of conductor is the obstruction posed by the conductor to the flow of electric current. Its unit is Ohm and denoted by Ω. 1 Ω is the resistance of conductor if 1 A flows through a conductor when potential difference of 1 Volt is applied
Resistivity (ρ) is also defined as resistance of cube of unit dimensions. Unit of resistivity is W-m. Inverse of resistivity is called conductivity (SI mho m-1) and Inverse of resistance is conductance (Unit Mho or Siemen). Resistivity is a property of material, does not depend on physical dimensions. But resistance does depend on physical dimensions.
Resistivity of conductor, hence resistance of conductor does vary with temperature given by
RT = RO (1 + αT),where R0 is resistance at 00C and RT is resistance at temperature T. if we see the mathematical form of resistivity we can see that it depends on relaxation time, which decreases when temperature is increased. ‘α’ is called temperature coefficient of resistance and defined as change in resistance of 1 Ω when temperature is changed by 10C
‘α’ is positive for metals, negative e for semiconductor, and almost zero for some alloys, i.e. constantan, eureka and manganin. Second property of these alloys is higher resistivity. Heater element is made from alloy (63% Tin, 37%Lead) (high resistivity and also high melting point) and fuse wire is made from Nichrome (low resistivity and low melting point. Its unit is /0C
Thermistor has large α and is used to
(i) safe guard television picture tube
(ii) temperature control units in industry.
Superconductivity is phenomenon of almost zero resistivity, it can be achieved at very low temperature (as atoms just freeze and no collision occurs with electron for moving one point to other) At that temperature (critical temperature) substance is referred as superconductor.
COMPARISON of Electrical conductivity of metals and electrolysis
In Metals the conduction is done by electrons
(i) They are small in size
(ii) Large in number (Recall Avogadro Number)
While in Electrolytes
(i) Ions (Charge carrier) are large
(ii) Number is small ( Degree of dissociation )
(iii) Viscosity
Due to these the conduction is better in metals as compared to electrolyte
To indicate the value of resistance and its tolerance colored lines are drawn on resistance. Value of resistance can be calculated. 1st 2 colors give numeric value, 3rd give number if zeros that follow the value. And 4th gives the tolerance. 1st can be of any color from given below but 4th will be either gold, silver or no color. Values are tabulated as:
| Black | Brown | Red | Orange | Yellow | Green | Blue | Violet | Grey | White | Gold | Silver | No col. |
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ± 5% | ± 10% | ±20% |
E.g. if colors are yellow violet orange silver: 47´103 ± 10% Ω [1st color cannot be Black]
Above table is remembered as is remembered as BB Roy of Great Britain had Very Good Wife
Resistance Grouping: Resistance can be grouped in series and parallel
For series we have same current in circuit
Internal cell: when current flows in a circuit due to a battery attached, the electrons start from –ve of battery and after passing through conductor reach +ve terminal of battery. Then after this electron move from +ve terminal to –ve within battery. The obstruction caused by contents within the cell is called internal resistance and denoted by ‘r’. it depends on
(i) distance between electrode
(ii) nature of electrolyte
(iii) nature of electrode. The energy or work done by the electron to move from negative of battery to again positive of battery via conductor is provided by the cell. This work is done at the cost of losing its chemical energy.
Terminal potential is defined as the Pd. across its terminals when current is flowing (closed circuit)
Emf is defined as the potential difference across its terminals when current is not flowing (open circuit)
While discharging the cell i.e. when cell is providing current
V = E – Ir and while charging V = E + Ir.
Clearly when cell is discharge E > V, when cell is charged E < V and when no current flowing E = V
Difference between emf & terminal potential difference
| EMF of cell
1. The emf of cell is the maximum potential difference between two electrodes when the cell is in open circuit. 2. It is independent of resistance of circuit and depends on nature of electrodes and electrolytes. 3. It is source of electric current in the circuit. 4. It is cause |
Terminal Pd
1. The emf of cell is the maximum potential difference between two electrodes when the cell is in a closed circuit. 2. It is dependent on resistance of circuit and depends on nature of electrodes and electrolytes 3. It is available Pd in external circuit. 4. It is an effect
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