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Resistance and Resistivity

V1 L of solut...

Question

$V_{1}$ L of solution A (resistance 500ohm) is mixed with $V_{2}$ L of solution B (Resistance 100ohm) resistance of final solution is 80 then $V_{2}$ / $V_{1}$ :

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Solution

Since both solution has different density so they separated parallely.

$\frac{V_{1}}{R_{1}} + \frac{V_{2}}{R_{2}} = \frac{V_{1} + V_{2}}{R e g .}$

$\frac{V_{1}}{50} + \frac{V_{2}}{100} = \frac{V_{1} + V_{2}}{80}$

$80 (100 V_{1} + 50 V_{2}) = 5000 V_{1} + 5000 V_{2}$

$8000 V_{1} + 4000 V_{2} = 5000 V_{1} + 5000 V_{2}$

$(8000 - 5000) V_{1} = (5000 - 1000) V_{2}$

$3 V_{1} = V_{2}$

$\frac{V_{2}}{V_{1}} = 3$

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