1.

When two resistances R1 and R2 are connected in series, they consume 12W power. When theyare connected in parallel, they consume 50 W power. What is the ratio of the powers of R1 and R2?

Answer»

So for series connection equivalent resistance(R) = R1 + R2

for parallel connection equivalent resistance(r) = \frac{R1*R2}{R1+R2}

so we know P = VI ⇒ P = I²R 

so for series connection 12 = V²/R   ..... {i}

for parallel connection 50 = V²/r .............. {II}

dividing i from ii

so \frac{50}{12}= \frac{R}{r}

⇒ \frac{25}{6}= \frac{(R1+R2)^2}{R1R2}

⇒ 6R1² + 6R2² - 13R1R2 = 0

⇒  6R1² - 9R1R2 - 4R1R2 + 6R2²= 0

⇒ 3R1(2R1 - 3R2) - 2R2(2R1 - 3R2) = 0

⇒ (2R1 - 3R2)(2R1 - 3R2) = 0

so  \frac{R1}{R2}= \frac{3}{2},\frac{2}{3}   ANSWER
   


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