What is electrical resistance ? Its value depend on which factors ?

Explanation

`rArr` Property of opposing flow of charge in conductor is called resistivity.
`rArr ` From ohms law R = `(V)/(I)`. Its unit is `("Volt")/("Amp")` = ohm`(Omega)` . Its dimensional formula is `M^(1) L^(2) T^(-3) A^(-2)`.
`rArr ` Consider a conductro with length. l and area A as shown in figure (a).

`rArr` Such two similar rectangular block are shown in figure (b). Here, length of combination will be 2L
`rArr` Current flowing through combination of block will be equal to current flowing through each block. Hence, potential difference between two ends of each block will be V only.
` rArr` So for total two block potential differenc between ends of combination will be 2V.
` rArr` Let resistance combination of blocks be `R_(C)` the by Ohm.s law,
`R_(C) = (2V)/(I)` = 2R ....(1)
where `(V)/(I)= ` R = reistance of each block
`rArr` Thus, reistance of conductor is proportional its length. By making length double resistance will become double.
`therefore R prop l " " `....(2)
`rArr` let given block is cut into two equal parallel to length. in this case length of each part will be l and cross-section area will be `(A)/(2)`

` rArr ` Now blocks are arranged as shown in figure (c). Let potential difference between end o! combination be V and current flowing througt- combination be I then current flowing through
`rArr` each part will be `(I)/(2)`.
`rArr` Let resistance of each block be `R_(1)` then by Ohm law,
` R_(1) = (V)/((I)/(2)) = (2V)/(I) = 2R " ....(3)" [ because (V)/(I) = R ] `
`rArr` Thus, resistance of conductor is inversely proportional to its cross-sectional area, by changing cross-section area to `((A)/(2))` resistance will become double.
`therefore R prop (1)/(A)" "` ....(4)
where A = cross-section area comparing equation (2) and (4),
Resistance of given conductor.
`R prop (l)/(A)`
`therefore R = rho (l)/(A) " " `....(5)
`rArr` Thus, resistance of conductor depends on its length, cross-sectional area and type of material. p is proportionally constant. It is called resistivity.