Ohm’s law
(a) 
= constant called electrical resistance R, provided there is no change in the physical conditions like temperature, pressure & impurity etc.
(b) 
= (Microscopic version) i.e. conductivity of a conductor is independent of electric field existing in the material over a wide range of field.
^The magnitude of the difference between the individual measurement and the actual or true value is called the absolute error in the
measurement of that quantity. It is represented by 
The ratio of the absolute error to the actual quantity measured is called the relative error of the measurement.
Relative error 
Resistivity of conductors (ρ)
Resistance per unit length per unit cross sectional area of a material is called its resistivity or specific resistance, for metals it is (a) 
.
Its reciprocal is called conductivity or specific conductance (σ). Both ρ & σ are independent of length, thickness, & shape or geometry.
Continuity equation for Conductors
For a conductor of variable cross section
= constant at all sections but drift speed varies inversely with area of cross section.
Current mechanism in conductors
In metals about 10 29 m – 3 of free electrons (called average number density ‘n’ ) move randomly (disordered) in all directions (like motion of gas particles) with average thermal speed of about 105 m/s & collide randomly with the metal ions (almost fixed). Between the collision the free electrons travel along straight lines with average relaxation time (t) of about 10 – 14 s, however due to random motion net charge (electrons) crossing any imaginary plane is zero. On applying external potential difference across a metal an electric field is created in it, which exerts force on electron opposite to the direction of electric field & electron apart from thermal motion (disordered) now start drifting in a definite direction (opposite to the direction of electric field) . Using v – t eqn. the drift velocity of free electrons in metals is 
.
Average value of drift velocity of free electrons in metals is of the order of few mm /s. Drift velocity per unit applied electric field is called electron mobility (μ) i.e.
Let ‘n’ be the no. density (i.e. N/V) of free electrons of a metal, then current equation for metal slab of cross sectional area A is
1 A is the flow of 6.25 x 10 18 electrons per second.
Electric current (I) & current density (J)
Electric current is the rate at which electric charge crosses a plane. i.e. mathematically, 
Current per unit area is called current density, i.e. mathematically, 
Electric current is scalar, while current density is vector. I & J are parallel to applied E – field.
Wheatstone bridge
The arrangement of five capacitors as shown is called Wheat stone bridge.
If 
then points P & Q are at same potential & the bridge is said to be balanced, due to this no charge will flow in the arm PQ & hence arm PQ can be removed & circuit can becomes as shown.
The effective capacitance across the points X & Y for the balanced state of Wheatstone bridge is 
the bridge is not balanced, then the problem can be solved using Kirchoff’s laws.
Kirchoff’s laws
1st or junction rule: Σq = 0 at any isolated junction to conserve charge.
2nd or mesh rule: ΣV = 0 for any closed mesh to conserve energy.
For shown circuit we can write
At jn. A: – q1 + q2 + q3 = 0
Connecting or disconnecting battery
On disconnecting the battery charge remains constant & if the battery remains connected then potential difference across the capacitor remains constant. Using the above fact the effect of inserting a dielectric slab between plates of a capacitor can be expressed by the following table:
Parallel dielectrics in a capacitor
If three dielectric of slabs of same thickness, but different areas of cross section A1, A2 & A3 , dielectric constants K1, K2 & K3 are placed between the plates of a parallel plate capacitor as shown, then the combination behaves as different dielectrics dividing the plate area are considered as capacitors connected parallel.
Capacitance of this is given by
Cnet = C1 + C2 + C3
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