Question

A cylindrical rod of length L is connected across a fixed potential difference, creating a current I through the rod. What would be the current if the length of the rod were doubled?

2
1/4
1/2
4

Answer 1

The value of current through the rod becomes half

`i' = (i)/(2)`

Step-by-step explanation:

As per Ohm's law we know that the current through a resistor is given as

`i = (V)/(R)`

here we know that

`R = \rho (L)/(A)`

here we know that the length of the cylinder is L and area is A so the value of current through the rod is given as

`i = (V A)/(\rho L)`

now we have change the length of the conductor to twice of initial value and rest all parameters will remain the same

so we will have

`i' = (VA)/(\rho (2L))`

now from above two equations we have

`(i)/(i') = 2`

so new current will become

`i' = (i)/(2)`