Question

Two resistances $R_1$ and $R_2$ when connected in series consume power equal to $25W$. When connected in parallel they consume $100W$. The ratio of power of each is.

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $1$

Answer 1

Answer: (D)

$1$

$P_{R_1}+P_{R_2}=25P_{R_1}+P_{R_2}=100$

$I^2[R_1+R_2]=25E^2[\frac{1}{R_1}+\frac{1}{R_2}]=100$

$\frac{E^2}{(R_1+R_2)}=25$

$\Rightarrow 25(R_1+R_2{)}^2=100R_1{R}_2$

$\Rightarrow (R_1-R_2{)}^2=0$

$R_1=R_2$

$\frac{P_1}{P_2}=\frac{R_2}{R_1}=1$