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2 wires of same dimension but different resistivity(rho 1 & rho 2) are connected in series and after that in parallel,then the equivalent resistivity of the conductor in both the case will be?

2 wires of same dimension but different resistivity(rho 1 & rho 2) are connected in series and after that in parallel,then the equivalent resistivity of the conductor in both the case will be?

Grade:Upto college level

8 Answers

Chetan Mandayam Nayakar
312 Points
11 years ago

series: rho(series)= (rhoi+rho2)/2

parallel:rho(parallel)=(rho1)(rho2)/(rho1 + rho2)

Ritvik Agarwal
8 Points
11 years ago

R1=(rho1)L/A

R2=(rho2)L/A

In series; Req=(rho1+rho2)L/A =>Resistivity=(rho1+rho2)

In parallel; Req=((rho1)(rho2)/(rho1+rho2))L/A =>Resistivity=Req(parallel) X (A/L)

Chetan Mandayam Nayakar
312 Points
11 years ago

my previous solution was wrong. the correct answer is:

series: (rho1 + rho2)/2

parallel: (rho1*rho2)/(2*(rho1+rho2))

please inform me in case you want more explanation

anurag bhattacharjee
42 Points
11 years ago

yes sir ,i want to know how to approach and solve this question exactly instead of just knowing the answers.

xyz xz
37 Points
11 years ago

R1= ρ1(l/A)

R2= ρ2(l/A)

R= ρ(2l)/A

and Rs = R1+R2

» ρs = (ρ1+ρ2)/2

and Rp = (R1.R2)/(R1+R2)

» ρp = (1/2)(ρ1ρ2)/(ρ1+ρ2)

mahima
13 Points
5 years ago
First we can start with calculating the equivalent resisitance of the combination.  {R = rho*l/a}
rho*2*l/a = (rho 1+ rho 2)l/a
in this case since the dimensions of both the wires are same, the total length is considered for net resistance
So l/a gets cancelled on both sides and we have..
rho(total) *2 = rho 1 + rho 2
this implies that,
rho (total) = (rho 1 + rho 2)/2
Gitanjali Rout
184 Points
5 years ago
 

R1= ρ1(l/A)

R2= ρ2(l/A)

R= ρ(2l)/A

and Rs = R1+R2

» ρs = (ρ1+ρ2)/2

and Rp = (R1.R2)/(R1+R2)

» ρp = (1/2)(ρ1ρ2)/(ρ1+ρ2)

Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the solution to your problem below.
 
R1= ρ1(l/A)
R2= ρ2(l/A)
R= ρ(2l)/A
 
In series, Rs = R1+R2
→ ρs = (ρ1+ρ2)/2
 
In parallel, Rp = (R1.R2)/(R1+R2)
→ ρp = (1/2)(ρ1ρ2)/(ρ1+ρ2)
 
Hope it helps.
Thanks and regards,
Kushagra

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