Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length ${\mathcal{l}}_2$ is 40cm. Now as unknown resistance x is connected in series with P and new balancing length is found to be 80cm measured from the same end. Then the value of x will be _________ $\mathrm{\Omega .}$

<p>Initially, &nbsp;<math><mrow><mfrac><mrow><mi>P</mi></mrow><mrow><mi>Q</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mn>0</mn></mrow><mrow><mn>6</mn><mn>0</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></math>&nbsp;- (1)</p><p>Finally, &nbsp;<math><mrow><mfrac><mrow><mi>P</mi><mo>+</mo><mi>x</mi></mrow><mrow><mi>Q</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>8</mn><mn>0</mn></mrow><mrow><mn>2</mn><mn>0</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>1</mn></mrow></mfrac></mrow></math></p><p> (2) (1)</p><p><math><mrow><mfrac><mrow><mi>P</mi><mo>+</mo><mi>x</mi></mrow><mrow><mi>P</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mo>×</mo><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>=</mo><mn>6</mn></mrow></math></p><p><math><mrow><mo>⇒</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mi>x</mi></mrow><mrow><mi>P</mi></mrow></mfrac><mo>=</mo><mn>6</mn></mrow></math></p><p><math><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>P</mi></mrow></mfrac><mo>=</mo><mn>5</mn></mrow></math></p><p>x = 5 P = 5 x 4 = 20 <math><mrow><mi>Ω</mi></mrow></math></p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment