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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Experimental Physics

NTA Abhyas 2020 · Physics · Experimental Physics

A standard cell of 1.08V is balanced by the potential difference...

A standard cell of 1.08V1.08V is balanced by the potential difference across 90cm90cm of a 11 meter, long wire supplied by a cell of emf 2V2V through a series resistor of resistance 2Ω2Ω. If the internal resistance of cell in the primary circuit is zero then the resistance per unit length (in Ωm−1Ω{m}^{- 1}) of potentiometer wire isA standard cell of 1.08V is balanced by the potential difference across 90cm of a 1 meter, long wire supplied by a cell

Correct answer

3

Step-by-step solution

A standard cell of 1.08V is balanced by the potential difference across 90cm of a 1 meter, long wire supplied by a cell

E=X.l(X=Potentialgradient)E = X . l( X = \text{Potential}\text{gradient} )

E=(EoL×RwRw+r+Rh)×l(∵r=0,Rh=2Ω)E = \left(\dfrac{{E}_{o}}{L} \times \dfrac{{R}_{w}}{{R}_{w} + r + {R}_{h}}\right) \times l\left(∵ r = 0, {R}_{h} = 2Ω\right)

∴1.08=(21m×RwRw+2)×0.90m∴ 1.08 = \left(\dfrac{2}{1m} \times \dfrac{{R}_{w}}{{R}_{w} + 2}\right) \times 0.90m

1.082×0.90=RwRw+2\dfrac{1.08}{2 \times 0.90} = \dfrac{{R}_{w}}{{R}_{w} + 2}

Hence : 0.6=RwRw+20.6 = \dfrac{{R}_{w}}{{R}_{w} + 2}

0.6Rw+1.2=Rw⇒1.2=0.4Rw⇒3=Rw0.6{R}_{w} + 1.2 = {R}_{w} ⇒ 1.2 = 0.4{R}_{w} ⇒ 3 = {R}_{w}

∴∴ Resistance per unit length is 3Ωm−13Ω{m}^{- 1}
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