Two metallic wires of identical dimensions are connected in series. If <math><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>a</mi><mi>n</mi><mi>d</mi><mtext> </mtext><mtext> </mtext><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> are the conductivities of these wires respectively, the effective conductivity of the combination is:

R = R1 + R2 ⇒ 2 l σ A = l σ 1 A + l σ 2 A ⇒ 2 σ = 1 σ 1 + 1 σ 2 ⇒ σ = 2 σ 1 σ 2 σ 1 + σ 2

Two metallic wires of identical dimensions are connected in series. If&nbsp;<math><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>a</mi><mi>n</mi><mi>d</mi><mtext> </mtext><mtext> </mtext><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>&nbsp;are the conductivities of these wires respectively, the effective conductivity of the combination is:

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Physics NCERT Exemplar Solutions Class 12th Chapter Nine Physics Class 12th Physics NCERT Exemplar Solutions Class 12th Chapter Three

Two metallic wires of identical dimensions are connected in series. If $σ_{1} a n d σ_{2}$ are the conductivities of these wires respectively, the effective conductivity of the combination is:

Option 1 -

$\frac{σ_{1} σ_{2}}{σ_{1} + σ_{2}}$

Option 2 -

$\frac{2 σ_{1} σ_{2}}{σ_{1} + σ_{2}}$

Option 3 -

$\frac{σ_{1} + σ_{2}}{2 σ_{1} σ_{2}}$

Option 4 -

$\frac{σ_{1} + σ_{2}}{σ_{1} σ_{2}}$

5 Views | Posted 2 months ago

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1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 2

Detailed Solution:

R = R1 + R2

$\Rightarrow \frac{2 l}{σ A} = \frac{l}{σ_{1} A} + \frac{l}{σ_{2} A} \Rightarrow \frac{2}{σ} = \frac{1}{σ_{1}} + \frac{1}{σ_{2}} \Rightarrow σ = \frac{2 σ_{1} σ_{2}}{σ_{1} + σ_{2}}$

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Two metallic wires of identical dimensions are connected in series. If $σ_{1} a n d σ_{2}$ are the conductivities of these wires respectively, the effective conductivity of the combination is: