How is resistance and resistivity affected if length of the wire is doubled.
The Resistivity of the wire will not change with the change in length. Resistivity is a property of the wire, it doesn't depend upon it’s length or cross-sectional area.
However, If you are asking about Resistance, it will increase to 4 times it’s initial value.
Resistance,R = ρl/A
Where,
- ρ=Resistivity of the wire
- l=lenght of wire
- A= cross section of the wire
So, now if you increase the length of wire by 2 times it’s cross-sectional area will decrease by 2 times, because the volume of the wire has to remain constant.
Let, the initial and final radius of the wire be r1,&r2 respectively.
Since the initial and final volume are equal, so
2π(r1^2)l = 2π(r2^2)(2l)
So, r2=r1/√2
So, the cross-sectional area becomes 1/2 times the initial value.
Putting the values in the formula for resistance, we get the new resistance 4 times greater than the initial values of resistance
The Resistivity of the wire will not change with the change in length. Resistivity is a property of the wire, it doesn't depend upon it’s length or cross-sectional area.
However, If you are asking about Resistance, it will increase to 4 times it’s initial value.
Resistance,R = ρl/A
Where,
- ρ=Resistivity of the wire
- l=lenght of wire
- A= cross section of the wire
So, now if you increase the length of wire by 2 times it’s cross-sectional area will decrease by 2 times, because the volume of the wire has to remain constant.
Let, the initial and final radius of the wire be r1,&r2 respectively.
Since the initial and final volume are equal, so
2π(r1^2)l = 2π(r2^2)(2l)
So, r2=r1/√2
So, the cross-sectional area becomes 1/2 times the initial value.
Putting the values in the formula for resistance, we get the new resistance 4 times greater than the initial values of resistance
