Saved Bookmarks
| 1. |
What is electrical resistance ? Its value depend on which factors ? |
|
Answer» Solution :`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. |
|