Question

When two unknown resistors are connected in series with a battery, $225W$ power is delivered to the combination with a total current $5A$. For the same total current $50W$ is delivered when the resistors are connected in parallel. Find the ratio of the two resistances.

• A. 2
• B. 5
• C. 4
• D. 10

Answer 1

The correct option is A 2

Here power delivered in series and parallel combinations is

$225=5^2(R_1+R_2)$ .........(1)

$50=5^2\left(\frac{R_1{R}_2}{R_1+R_2}\right)$ ..........(2)

comparing equations (1) and (2), we get

$\frac{(R_1+R_2{)}^2}{R_1{R}_2}=\frac{225}{50}=\frac{9}{2}$

$\frac{R_1^2(1+\frac{R_2}{R_1}{)}^2}{R_1{R}_2}=\frac{9}{2}$

Put, $\frac{R_1}{R_2}=x$

$x(1+\frac{1}{x}{)}^2=\frac{9}{2}$

$x(\frac{x+1}{x}{)}^2=\frac{9}{2}$

$x^2+2x+1=\frac{9x}{2}$

$2x^2-5x+2=0$

Taking roots of equation we get

$x=2$

$\therefore \frac{R_1}{R_2}=2$