Question

Two wire of same length and thickness has specific resistance 6 ohm cm and 3 ohm cm connected in parallel. Effective resistivity is rho ohm cm. What is the value of rho ohm cm? ​

Answer 1

Answer:

4

Explanation:

EQUIVALENT RESISTIVITY = (6×3)/9=2

AS THE RESISTIVITY OF A GIVEN WIRE HAS SAME LENGTH AS THE INDIVIDUAL BUT AREA IS DOUBLED .SO THE EQUIVALENT RESISTIVITY IS 2×2=4.

Answer 2

Answer:

The effective resistivity is 4Ωcm.

Resistors in parallel:

• Resistors are said to be in parallel if their end terminals are connected to the same nodes.
• In parallel combination, the overall resistance is smaller than the individual resistances.
• Hence, a parallel combination is used to reduce the resistance of the circuit.

Specific Resistance:

• Specific resistance is defined as the resistance of a material of unit length and unit area of cross-section.
• Specific resistance is also called resistivity and is denoted as ρ.
• It is given by the formula $\frac{RA}{l}$, where R is the resistance.

Explanation:

Given: ρ1 = 6Ωcm, ρ2 = 3Ωcm

To find: Effective resistivity ρ

Formula: $R=\frac{R_{1}R_{2} }{R_{1}+R_{2} }$ and ρ $=\frac{RA}{l}$

Step 1:

Rearranging the second formula,

$R=(\frac{l}{A})$ ρ

Step 2:

Substituting the above equation in parallel combination formula, we get

$(\frac{l}{2A} )$ ρ $=[( \frac{l}{A} )$ ρ1 $( \frac{l}{A} )$ρ2$]$ / $[( \frac{l}{A} )$ρ1$+( \frac{l}{A} )$ρ2$]$

ρ/2 = (ρ1 ρ2) / (ρ1 + ρ2)

Step 3:

Substituting the given values

ρ/2 = $\frac{(6)(3)}{6+3}$

ρ/2 = $\frac{18}{9}$

ρ = $\frac{(18)(2)}{9}$

ρ = 4

Therefore, the effective resistivity is 4Ωcm.

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