A potentiometer wire of length 300 cm is connected in series with a resistance 780 $\Omega$ and a standard cell of emf 4V. A constant current flows through potentiometer wire. The length of the null point for cell of emf 20 mV is found to be 60 cm. The resistance of the potentiometer wire is ________ $\Omega$ .

<p>&nbsp;<math><mrow><mi>I</mi><mo>=</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mi>R</mi><mo>+</mo><mn>7</mn><mn>8</mn><mn>0</mn></mrow></mfrac></mrow></math></p><p>Potential Difference across AB = l × R =&nbsp;<math><mrow><mfrac><mrow><mn>4</mn><mi>R</mi></mrow><mrow><mi>R</mi><mo>+</mo><mn>7</mn><mn>8</mn><mn>0</mn></mrow></mfrac></mrow></math></p><p>Potential Difference across AC =&nbsp;<math><mrow><mrow><mo> (</mo><mrow><mfrac><mrow><mn>4</mn><mi>R</mi></mrow><mrow><mi>R</mi><mo>+</mo><mn>7</mn><mn>8</mn><mn>0</mn></mrow></mfrac></mrow><mo>)</mo></mrow><mo>×</mo><mfrac><mrow><mn>6</mn><mn>0</mn></mrow><mrow><mn>3</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mrow></math></p><p><math><mrow><mo>⇒</mo><mfrac><mrow><mn>4</mn><mi>R</mi></mrow><mrow><mn>5</mn><mrow><mo> (</mo><mrow><mi>R</mi><mo>+</mo><mn>7</mn><mn>8</mn><mn>0</mn></mrow><mo>)</mo></mrow></mrow></mfrac><mo>=</mo><mn>2</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>⇒</mo><mi>R</mi><mo>=</mo><mn>2</mn><mn>0</mn><mi>Ω</mi></mrow></math></p>

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