Two wire of same length and area ,made of two materials of resistivity T1 ana T2 are connected in parallel with voltage sourceof potential V.The euivalent resistivity for same length and area is *
Answers
Answer:
Two wires of same length and area made of two materials of resistivity \rho_1\ and\ \rho_2ρ
1
and ρ
2
. The equivalent resistance of resistors in series combination is given by :
R_{eq}=R_1+R_2R
eq
=R
1
+R
2
Since,
R=\rho\dfrac{l}{A}R=ρ
A
l
...........(1)
Where
length and area of two materials are same
\dfrac{\rho_{eq}l}{A}=\dfrac{\rho_1l}{A}+\dfrac{\rho_2l}{A}
A
ρ
eq
l
=
A
ρ
1
l
+
A
ρ
2
l
So,
\rho_{eq}=\rho_1+\rho_2ρ
eq
=ρ
1
+ρ
2
The equivalent resistance of resistors in parallel combination is given by :
\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}
R
eq
1
=
R
1
1
+
R
2
1
Using equation (1) we get :
\dfrac{A}{\rho_{eq} l}=\dfrac{A}{\rho_1 l}+\dfrac{A}{\rho_2 l}
ρ
eq
l
A
=
ρ
1
l
A
+
ρ
2
l
A
So,
\dfrac{1}{\rho_{eq}}=\dfrac{1}{\rho_1}+\dfrac{1}{\rho_2}
ρ
eq
1
=
ρ
1
1
+
ρ
2
1
Hence, this is the required solution.