Question

Two insulated copper wires of similar overall diameter have very different interiors. One wire possesses a solid core of copper, with a circular cross section of radius 1.53 mm. The other wire is composed of 19 strands of thin copper wire bundled together. Each strand has a circular cross section of radius 0.306 mm. The current density ???? in each wire is the same. ????=1750 A/m2 Two circles. One circle is solid, whereas the other contains 19 tightly packed smaller circles How much current does each wire carry? solid wire current: A stranded wire current: A The resistivity of copper is ????=1.69×10−8 Ω·m. What is the resistance of a 3.25 m length of each wire? solid wire resistance: Ω stranded wire resistance: Ω

Answer 1

a

Solid Wire
`I  =   0.01237 \  A`

Stranded Wire
`I_2  =   0.00978 \  A`

b

Solid Wire
`R  = 0.0149 \ \Omega`

Stranded Wire
`R_1  = 0.0189 \ \Omega`

Step-by-step explanation:

Considering the first question

From the question we are told that

The radius of the first wire is
`r_1  = 1.53 mm = 0.0015 \  m`

The radius of each strand is
`r_0 =  0.306 \ mm =  0.000306 \ m`

The current density in both wires is
`J  =  1750 \  A/m^2`

Considering the first wire

The cross-sectional area of the first wire is

`A   = \pi  r^2`

= >
`A   = 3.142 *  (0.0015)^2`

= >
`A   = 7.0695 *10^(-6) \  m^2`

Generally the current in the first wire is

`I  =  J*A`

=>
`I  =  1750*7.0695 *10^(-6)`

=>
`I  =   0.01237 \  A`

Considering the second wire wire

The cross-sectional area of the second wire is

`A_1  =  19 *  \pi r^2`

=>
`A_1  =  19 *3.142 *  (0.000306)^2`

=>
`A_1  =  5.5899 *10^(-6) \  m^2`

Generally the current is

`I_2  =  J  *  A_1`

=>
`I_2  =   1750  *  5.5899 *10^(-6)`

=>
`I_2  =   0.00978 \  A`

Considering question two

From the question we are told that

Resistivity is
`\rho  =  1.69* 10^(-8) \Omega \cdot m`

The length of each wire is
`l =  6.25 \  m`

Generally the resistance of the first wire is mathematically represented as

`R  =  (\rho *  l  )/(A)`

=>
`R  =  (  1.69* 10^(-8) * 6.25 )/( 7.0695 *10^(-6) )`

=>
`R  = 0.0149 \ \Omega`

Generally the resistance of the first wire is mathematically represented as

`R_1  =  (\rho *  l  )/(A_1)`

=>
`R_1  =  (  1.69* 10^(-8) * 6.25 )/(5.5899 *10^(-6) )`

=>
`R_1  = 0.0189 \ \Omega`