Question

if R1 and R2 are the resistance of two resistors having power 50W and 100W respectively designed to operate same voltage then R1/R2 is​

Answer 1

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Answer 2

Answer:

The value of R1/R2 is​ 2.

Explanation:

• Electric power: Power is work done per unit time and its SI unit is Watt(W). The formula for power can be written as, Power(P) = $\frac{V^2}{R}$

       where V is the voltage and R is the resistance.

• Ratio calculation: In both the resistors applied voltage is same, suppose the voltage is V.

       For $R_1$ resistor, Power = $P_1 = \frac{V^2}{R_1}$

       For $R_2$ resistor, Power = $P_2 = \frac{V^2}{R_2}$

     Power for two resistors are given as, $P_1$ = 50 W   and     $P_2$ = 100 W

     We can write,  $P_1$ : $P_2$ = 50 : 100

                            $\frac{\frac{V^2}{R_1}}{\frac{V^2}{R_2}}$   =    $\frac{50}{100}$  = $\frac{1}{2}$

                             $\frac{V^2}{R_1} \times {\frac{R_2}{V^2}}$  =  $\frac{1}{2}$

                                $\frac{R_2}{R_1}$ =  $\frac{1}{2}$    or, $\frac{R_1}{R_2}$ = $\frac{2}{1}$ = 2

  So, the value of R1/R2 is​ 2.

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