Two resistances R1 and R2 when connected in series and parallel with 120 V line, power consumed will be 25 W and 100 W, respectively. Then the ratio of power consumed by R1 to that consumed by R2 will be

# Two resistances R1 and R2 when connected in series and parallel with 120 V line, power consumed will be 25 W and 100 W, respectively. Then the ratio of power consumed by R1 to that consumed by R2 will be

1. A

1 : 1

2. B

1 : 2

3. C

2 : 1

4. D

1 : 4

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$\begin{array}{l}\mathrm{P}=\frac{{\mathrm{V}}^{2}}{\mathrm{R}}\text{\hspace{0.17em}}⇒\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\frac{{\mathrm{P}}_{\mathrm{P}}}{{\mathrm{P}}_{\mathrm{S}}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{{\mathrm{R}}_{\mathrm{S}}}{{\mathrm{R}}_{\mathrm{P}}}=\frac{\left({\mathrm{R}}_{1}+{\mathrm{R}}_{2}\right)}{{\mathrm{R}}_{1}{\mathrm{R}}_{2}\text{\hspace{0.17em}}/\text{\hspace{0.17em}}\left({\mathrm{R}}_{1}+{\mathrm{R}}_{2}\right)}\text{\hspace{0.17em}}=\frac{{\left({\mathrm{R}}_{1}+{\mathrm{R}}_{2}\right)}^{2}}{{\mathrm{R}}_{1}{\mathrm{R}}_{2}}\\ ⇒\text{\hspace{0.17em}\hspace{0.17em}}\frac{100}{25}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{{\left({\mathrm{R}}_{1}+{\mathrm{R}}_{2}\right)}^{2}}{{\mathrm{R}}_{1}{\mathrm{R}}_{2}}\text{\hspace{0.17em}}⇒\frac{{\mathrm{R}}_{2}}{{\mathrm{R}}_{1}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{1}{1}\end{array}$