Question

A copper wire and an iron wire of equal length l and diameter d are joined, and a potential difference V is applied between the ends of the composite wire. Calculate the potential difference (in volts) across the iron wire. Assume that l = 2.97 m, d = 0.88 mm, and V = 157 V.

Answer 1

The potential difference across the iron wire 134.2 V.

Step-by-step explanation:

Given that,

Length = 2.97 m

Diameter = 0.88 mm

Total potential = 157 V

We know that,

The resistivity of iron wire

`\rho_(i)=10*10^(-8)\Omega m`

The resistivity of copper wire

`\rho_(c)=1.7*10^(-8)\Omega m`

The voltage for each wire is proportional to the resistivity.

We need to calculate the resistance for copper wire

Using formula of resistance

`R_(c)=(\rho* l)/(A)`

Put the value into the formula

`R_(c)=(1.7*10^(-8)*2.97)/(\pi*(0.44*10^(-3))^2)`

`R_(c)=0.0830\ \Omega`

We need to calculate the resistance for iron wire

Using formula of resistance

`R_(i)=(\rho* l)/(A)`

Put the value into the formula

`R_(i)=(10*10^(-8)*2.97)/(\pi*(0.44*10^(-3))^2)`

`R_(i)=0.4883\ \Omega`

The total resistance is

`R =R_(c)+R_(i)`

`R=0.0830+0.4883`

`R=0.5713\ \Omega`

We need to calculate the potential difference across the iron wire

Using formula of potential difference

`V_(i)=(VR_(i))/(R)`

Put the value into the formula

`V_(i)=(157*0.4883)/(0.5713)`

`V_(i)=134.2\ V`

Hence, The potential difference across the iron wire 134.2 V.

Answer 2

The potential difference across iron wire is 133.95 V

Solution:

As per the question:

Length, l = 2.97 m

Diameter. d = 0.88 mm =
`0.88* 10^(- 3)\ m`

Voltage, V = 157 V

Now,

We know that the resistivity of iron,
`\rho_(I) = 10\ S`

Resistivity of copper,
`\rho_(I) = 1.72\ S`

Now,

The potential difference across the iron wire:

V' =
`(\rho_(I)V)/(\rho_(I) + \rho_(C))`

V' =
`(10* 157)/(10 + 1.72) = 133.95\ V`