Question

When two resistances ${{R}_{1}}$ and ${{R}_{2}}$ are connected in series, they consume $12 \,W$ power. When they are connected in parallel, they consume $50\, W$ power. What the ratio of the powers of ${{R}_{1}}$ and ${{R}_{2}}$ ?

• A. 44565
• B. 4
• C. 44622
• D. 3

Answer 1

Answer: (C)

44622

Answer 2

In series, ${{p}_{s}}=\frac{{{P}_{1}}\times {{P}_{2}}}{{{P}_{1}}+{{P}_{2}}}=12W$
In parallel, ${{P}_{p}}={{P}_{1}}+{{P}_{2}}=50\,W$
$\therefore$ ${{P}_{1}}{{P}_{2}}=12\times 50=600$
Now, ${{({{p}_{1}}-{{p}_{2}})}^{2}}={{({{p}_{1}}+{{p}_{2}})}^{2}}-4{{p}_{1}}{{p}_{2}}$
$={{(50)}^{2}}-4\times 600$
$=2500-2400=100$
$\therefore$ ${{P}_{1}}-{{P}_{2}}=10$
or ${{P}_{1}}=30W,{{P}_{2}}=20\,W$
$\therefore$ $\frac{{{P}_{1}}}{{{P}_{2}}}=\frac{3}{2}$